Man of Steel retroactively runs into this problem when later films reveal that most of the other members of the Justice League would have been on Earth and active as superheroes during Zod's invasion. With Batman it's justified, as without any of his tech that allowed him to go toe-to-toe with Superman in the sequel, he likely couldn't have done much anyway. No word on why Wonder Woman, Aquaman, or the Flash couldn't help out, though. Aquaman does have a subtle exception as The Ghost: Word of God is that he summoned the pod of whales that helped Kal-El ashore after the latter rescued rig workers from an exploding oil platform, but he wasn’t actually seen doing this by the audience, nor was his involvement alluded to in the film itself.
Justice League provides some clues: Arthur Curry limited himself to helping out a poor fishing village in Iceland (and he already wanted to avoid attracting attention prior to that when destroying an underwater robot in Batman v Superman), and Flash had no experience of confronting anything stronger than mere humans who can't do anything against his superior speed. Seeing Kryptonians trade super heavy blows and displaying superhuman speed themselves on TV might have dissuaded him from intervening. Still no word on why Diana didn't jump in other than maintaining her decision to not intervene in earthly affairs (the decision to greenlight Wonder Woman and have her appear in Batman v Superman came after the release of Man of Steel).
The Flash reveals that Barry was present in Metropolis, but as he had only just gotten his powers, he was only able to save a single child.
Averting this drives a lot of the conflict in Batman v Superman: Dawn of Justice. Gotham is a direct sister city to Metropolis, separated by the baynote Supplementary materials reveal that this Gotham is in New Jersey, and this Metropolis is in Delaware, so the geography fits. Wayne Industries has almost as much investment in Metropolis as Lex Corp and it's shown that the building Zod destroyed with his heat vision in the climax of Man of Steel was Wayne Financial. In addition to that, Bruce Wayne was there that day, knew many of the employees personally, and he blames Superman for the entire incident. The film continues to acknowledge that Superman's "area of operation" is far larger than just Metropolis, and is seen doing heroic acts around the world.
Suicide Squad: Neither Batman, the Flash, nor Wonder Woman showed up in Midway City when Enchantress and her brother began building a world-ending super-weapon smack dab in the middle of it. Even when a squad of villains Batman and the Flash locked up are let loose in the city with the Joker not far behind, there's not a superhero in sight. It's somewhat justified for Wonder Woman here, as her film shows her working at the Louvre museum in Paris, she returned to Europe soon after Clark's funeral. Given the time it takes to cross the Atlantic, and the unlikeliness of booking a seat on a plane one day or less before it leaves, the Midway City crisis would have been over by the time she gets there.
Justice League oddly enough does this despite being the series' first Crisis Crossover. Specifically, the Green Lantern Corps are shown as one of the groups fighting the Big Bad's army in the flashback, only to not be mentioned again. Why they don't show to stop the Big Bad in the present day is never addressed.
Aquaman: Arthur Curry/Aquaman never thinks to warn the Justice League in case Orm would invade the surface (they wouldn't be as effective as Aquaman underwater, to be fair). No member of the Justice League is ever shown responding to the tsunamis and massive dumpings of warships and trash Orm sends as a warning to the surface or at least asking Aquaman what's going on. Concept art has confirmed that there were plans for Batman (and possibly other members of the Justice League) to appear and help fight off Orm's invasion at one point, but this idea was scrapped for unknown reasons. Presumably, Ben Affleck's growing disinterest in the Batman role due to his personal problems at the time played a part in the cameo being cut.
SHAZAM!: The Justice League doesn't show up when Dr. Sivana and demons representing the Seven Deadly Sins invade Fawcett City and kill a bunch of people, forcing Billy Batson and his family to save the day. Superman shows up in the ending where Billy contacted him and convinced him to make a public appearance at his school.
Birds of Prey: Curiously, Batman and the Joker don't get involved in any of the events on their own turf, whether it be Harley Quinn blowing up a factory, a $500K bounty being issued for Cassandra Cain, Huntress's targeted killings across the city, Black Mask approaching hand's grasp of financial control over Gotham, and an army of gangs being sent after the titular Birds (the real life reason being that Ben Affleck had been on an extended hiatus from playing DCEU Batman and Warner Bros has been distancing themselves from Jared Leto as DCEU Joker).
At the end of Zack Snyder's Justice League, recurring character Calvin Swanwick reveals himself to be the Martian Manhunter in disguise. Why he didn't help out during Zod's attack on Metropolis, Doomsday's rampage or Steppenwolf's invasion isn't addressed.note The real world reason is that the ending scene was originally supposed to feature the John Stewart version of Green Lantern, whose prior absence could've been handwaved as him having been in deep space when those incidents occurred. When Snyder was denied permission to execute that original plan, he replaced Green Lantern with Martian Manhunter at the last minute so the ending could still feature the debut of another classic Justice League member from the comics.
During the finale of The Suicide Squad, Starro, a gigantic Kaiju, goes on a rampage through Corto Maltese and has to be taken down by the surviving members of Task Force X. The possibility of the Justice League or any other superheroes intervening is never once raised, though in this case it's justified since the mission was supposed to be covert, meaning by the time the outside world got wind of what was going on, the conflict was already over and the fact that one of the Task Force X members, Bloodsport, had put Superman in the ICU with a Kryptonite bullet. However, said hospitalisation may have happened further in the past, because not too long after Superman was seen with three other Justice League members, called in to assist Peacemaker's team on their mission, but missing the main event.
Black Adam introduces the Justice Society of America, who, according to supplementary material, were formed many years before Superman's public debut in Man of Steel. While the team itself disbanded some time ago (and two of the four new members are too young to have been involved in any previous stories), the surviving members like Hawkman and Doctor Fate were never seen or even mentioned in prior movies. The Justice League doesn't show up to help Black Adam or the Justice Society defend Kahndaq from Intergang and Sabbac. Superman appears in The Stinger to help Amanda Waller prove to Black Adam that there are people strong enough to keep him in check if he misbehaves. Though, the Justice Society being called in when Waller's has her ownteam makes sense considering most of the members making up those teams are either dead, freed, or in Peacemaker's case, already assigned on a mission.
SHAZAM! Fury of the Gods: The Justice League doesn't show up when the Daughters of Atlas invade Fawcett City with a bunch of monsters and kill a bunch of people, again forcing the Shazam family to save the day. It is revealed that Billy sent a message to Wonder Woman, but she only shows up after the battle is over, then uses her powers to bring Billy back to life and restore the powers of those who lost them.
The opening scene of The Flash features Batman and Flash teaming up, with Superman's absence justified due to him dealing with a volcanic eruption in Guatemala. Wonder Woman, however, does appear to help out. Justified later on in the film, as the altered timeline Barry accidentally creates means that most of the Justice League don't exist, with Aquaman never having been born, Cyborg still being a civilian football player, and Superman having been killed by General Zod as a baby. It's because of the Justice League's absence that Flash ultimately teams up with Supergirl, the older Michael Keaton version of Batman, and his own teenage self in order to stop Zod from destroying the planet.
Aquaman and the Lost Kingdom: Arthur/Aquaman needs to get Orm out of his prison without the jailbreak being connected to Atlantis. For some reason, outsourcing the job to a non-Atlantean superhero never occurs to anyone. Then he again does not call in the Justice League when Black Manta and his forces start dangerously raising the temperature of the environment or when it's time to go stop Manta once and for all in Necrus. And, by the end, while superheroic presence is not required, no superhero shows up to welcome the people of the Seven Seas when they eventually reveal their existence to the world.
The plot of the first season involves Amanda Waller assembling a team of ARGUS operatives to take down an outright Alien Invasion, but the titular Peacemaker is the only Suicide Squad member she bothers sending with them. It's eventually revealed that this is entirely intentional on her part. As the mission involves killing multiple high profile targets that have been replaced by the aliens (politicians, celebrities, etc), Waller's intention was to have Peacemaker act as the Fall Guy after the threat was neutralized. Since he already has a reputation for being a mentally unstable loner, the authorities and public are quick to believe that he acted on his own without any assistance from the government.
Played for Laughs in the Season 1 finale. The members of the Justice League actually do show up this time... but arrive after Peacemaker and his pals have already killed the aliens. Peacemaker is understandably pissed by this.
