Pep Guardiola and Ole Gunnar Solskjaer condemned fans who made aeroplane gestures and threw seats during Wednesday’s Manchester derby.
A social media post showed fans in the Manchester City section making gestures referring to the 1958 Munich air crash, in which 23 people died, including eight United players.
After the match, fans in the United end threw seats at home supporters near by.
“I don’t know what happened but it is not nice,” said City boss Guardiola.
Manchester City, who won the Carabao Cup semi-final 3-2 on aggregate despite losing the second leg 1-0 at Etihad Stadium on Wednesday, did not comment but, as with previous cases of trouble, they will look at CCTV footage of the incidents and take the appropriate action.
Away allocations were cut by almost 50% for the two legs of the semi-final after problems at previous Manchester derbies.
“I have got to stand behind Pep,” said United boss Solskjaer.
“Football is a game we should all enjoy, spectators and the ones playing.
“We want rivalry but keep it at the same level. Let’s make sure we eradicate this now.”
Guardiola also said he was saddened at the attack by a group on the Cheshire home of executive vice-chairman Ed Woodward on Tuesday.
Woodward was at Wednesday’s game, before which, Solskjaer told Sky Sports that “everyone at the club is disgusted by what happened”.