So... how are the people of Rome going to take the death of Commodus? Sure the main characters (and the audience) might know how much of a monster he is but from what see he very much a Villain with Good Publicity to the average Roman. To all appearances Commodus was killed by a pre-planned coup by Maximus, Lucilla (who 'reveals' herself to be Maximus's lover by rushing to his side when Maximus is dying), Quintus and possibly Gracchus. Sure they might say they are following the wishes of Marcus Aurelius but he is inconviently dead.
Given that the new rulers are also in command of the entire army (plus Commodus having apparently never been particularly popular with his commanders), it probably doesn't matter what the people think because thinking against the killing would likely lead to becoming equally dead. Alternately, they wouldn't care as long as the new ruler didn't suck at his job. They didn't elect Commodus, so they probably wouldn't be that ticked off at his death.
Actually, the common people's opinion of Commodus seems to not be that good. Sure, they love the bread and circuses, but when Maximus rises in defiance, they side with him rather than the Emperor, as a few scenes show (their cheering forcing Commodus to spare Maximus in his first Coliseum fight, people calling him "Maximus the Merciful" for sparing a gladiator Commodus would have killed and the play with Maximus defying and defeating Commodus all being evidence of that). In fact, the only reason Commodus didn't have Maximus killed outside of the arena was because of how popular he was.