In Batman: Under the Red Hood, this is Ra's al Ghul's reaction when he realizes that The Joker killed Jason Todd - he just wanted the Joker to distract Batman, not take a young man's life.
In The Book of Life, Xibalba doesn't exactly say it, but the moment La Muerte angrily reminds him of the last wager he cheated on, he goes quiet. And looks at her with regret in his eyes and body movement.
Queen Elinor has a minor one when in an argument with her daughter Merida, she tossed Merida's treasured bow (a gift from her father) into the fireplace, causing Merida to run away sobbing. After Merida leaves, the bowstring makes a loud snap in the fireplace, causing Elinor to realize what she has destroyed - she even tearfully whispers "what have I done?!" She manages to fish it out, but it's too late. It's ruined, and so is her relationship with her daughter.
Later in the movie, Elinor gets this again when she reverts into the mind of a wild bear, and accidentally hurt her daughter and also her husband.
Merida has this herself from the point where she accidentally transforms Elinor into a bear until the end of the film. But it is only evident in the last few minutes, where it appears that Elinor has reverted to the wild bear state, and will never come back.
Brother Bear: Kenai has this feeling when he realizes that the bear he killed was Koda's mother. When he tells Koda about what happened, Koda doesn't take it well.
In Cars Doc Hudson after calling the press to take Lightning away to compete for the Piston Cup; Sally calls him out on his selfishness and everyone turns their backs on Doc as he is left alone at the broken traffic light.
Sally: You called them? Doc: It's best for everyone, Sally. Sally: Best for everyone... or best for you? [drives off]
Gill from Finding Nemo goes through one for nearly getting Nemo killed in one of his escape plans. He even apologizes for it face-to-face with the kid.
Nemo: Gill, I'm sorry I couldn't stop the— Gill: No, kid, I'm the one who should be sorry. I was so ready to get out, so ready to taste that ocean, I was willing to put you through harm's way to get there. Nothing should be worth that. I'm sorry I couldn't get you back to your father, kid.
In Finding Dory, Dory unwittingly ignores Marlin's pleas to keep her voice down around a dark area, and she, Marlin, and Nemo get chased by a giant squid that nearly eats Nemo. When Dory sees how shaken up Nemo was, she's horrified at what had happened, forgets what happened, and remembers when she sees Marlin comforting his son, murmuring apologies when Marlin gets angry at her.
After that, Marlin eventually regrets angrily telling Dory that forgetting was "what you do best".
At the climax of Disney's The Fox and the Hound, Tod saves Copper from a huge grizzly bear, and barely survives falling down a waterfall with it, leaving the fox, weak and exhausted, collapsing at the riverbank. Copper approaches, amazed Tod—the very fox he tried to hunt—saved his life, despite everything that happened, and now feels genuinely remorseful for what he's done to him. Then he steps in between Amos' gun & Tod refusing to move away, and Amos lowers his gun.
In Frozen, Elsa says this almost word-for-word when she is locked in a dungeon and looks out the window to see the endless winter she has (inadvertently) caused.
In G-Force Speckles. says almost word-for-word after realizing that he nearly destroyed the ones who truly care about him..
In Home, Oh, when he realizes how wrong his race was to invade the Earth, and then later that Gorg was only after the Boov because they stole his species' entire next generation.
In Hoodwinked the wolf utters this phrase after giving coffee to his hyperactive squirrel partner so that he can run quickly and tell the police that the rabbit is the villain.
How to Train Your Dragon: Stoick gets one of these after he disowns Hiccup for fraternizing with a dragon, and when he realizes that Hiccup was telling the truth about the Green Death and he's just doomed everyone with him.
During the climax of Inside Out, Anger gets a particularly painful one after realizing that the idea he's given Riley to run away back to Minnesota has triggered an all-consuming depression that he, Disgust, and Fear are powerless to stop.
Fear: Guys, we can't make Riley feel anything. Anger:[beat] What have we done?
King Triton says this almost world for word in The Little Mermaid, when he believes his argument with Ariel and destroying her human artifacts led to her running away. The look on his face immediately after said occurrence when she's reduced to tears can count as well.
Sebastian too after he "betrayed" Ariel after accidentally blurting out her love for a human to the king, which lead to the aforementioned incident.
Ursula had her moment after learning in shock that she killed her pet eels Flotsam and Jetsam with the trident by accident (thanks to Ariel yanking her hair), even mourning for their deaths before turning her rage towards Ariel for it.
Marty says this word for word when he realizes that his bringing his friends into the wild caused Alex to almost revert to his predatory instincts and leave them.
Megamind thinks this after seeing Hal/Titan using his powers for his own purpose. Instead of creating a new hero for Metro City, he made a villain far worse than him.
In Mickey's Twice Upon a Christmas, Mickey has this reaction when he realizes that him punishing Pluto for messing up his decorations led to him running away.
Mickey: Oh Pluto, if only I hadn't yelled at you. I swear I'll never raise my voice again.
In Monsters, Inc., although he doesn't say the actual words Sulley's reaction to accidentally terrifying Boo during his scaring demonstration, and by extension the other human children he has similarly terrified as the monster world's 'top scarer', is basically this.
Interestingly, the second half of the song subverts this. Jack starts off miserable, then turns bitter ("Why does nothing ever turn out like it should?"), then suddenly triumphant ("Well, what the heck?!/I went and did my best/And by God, I really tasted something swell!") before rushing off to fix his mistakes at the end.
In ParaNorman Judge Hopkins and the other zombies have this after they first died. As zombies they realize they were just foolish and scared of an innocent little girl who could talk to the dead, so they spend the movie trying to make up for it. Even at the end of the movie, their spirits still look regretful for what they did.
In Pocahontas, Thomas has this moment during the Villain Song "Savages" after he shot Kocoum to save John Smith's life. Not only does John Smith takes the blame for the murder, as well as sentenced to death at sunrise, but it caused war on both the Powhatan Tribe and the Settlers. His look on his face pretty much says it all.
In The Prince of Egypt, Moses accidentally pushes a slave overseer off a scaffolding to his death whilst saving an old Hebrew from being beaten brutally. He immediately has that reaction before deciding to exile himself out of guilt.
Cellach, in The Secret of Kells. As the sacking of Kells begins, it begins to get through to the Abbot that, despite all his preparation, things aren't going to work out. And what follows is a massive slaughter that basically makes the rest of his life one really prolonged version of this trope.
Sintel: The main character has spent years searching for her missing friend, a baby dragon, and killing the adult dragon that kidnapped it. Sadly, more years had passed than she realized, and she ends up killing her now adult dragon friend by mistake.
TMNT has one of these with Raphael in his battle against Leonardo, which is luckily averted just in time. Raph was dangerously close to killing Leo after a fiery battle, under the impression that Leo left him to be a show-off; the realization causes him to run away in fear.
In Toy Story, Slinky paraphrases this when he and the other toys see Woody and Buzz riding toward the moving truck and realize Woody was telling the truth. Downplayed with this Played for Laughs line:
When the characters of Sugar Rush realize who Vanellope really is, everyone panics, especially the other racers. Of course, they never realized the truth since their code had been manipulated by King Candy/Turbo.
Ralph gets his own, threefold: once when he smashes Vanellope's car on King Candy/Turbo's request, again when he realizes his game-jumping will cause his game to become unplugged since now Felix has gone after him and hasn't returned, and finally when he realizes that it is his fault that the Cy-Bugs from Hero's Duty have invaded Sugar Rush.
After Judy says at a press conference that predators going savage is in their nature, submerged predator/prey tensions rise to the surface causing civil unrest, and Nick is left feeling hurt and betrayed leading to their Plot-Mandated Friendship Failure. Seeing all this causes Judy to regret her ignorant remarks.
When Chief Bogo demands that Judy surrender her badge, Nick is seen looking surprised and guilty as he sees the consequences of his wasting Judy's time. This leads him to give Chief Bogo a What the Hell, Hero? speech where he reminds him that they still have ten hours left and still have a case to solve.