A pocket of City fans could be heard chanting after referee Michael Oliver blew his whistle to signal a moment's reflection in memory of the 97 Liverpool supporters who died at a 1989 FA Cup semifinal against Nottingham Forest.
The noise triggered an angry reaction from the Liverpool end as boos rang out in response, and a City spokesperson said: "Manchester City are extremely disappointed with the actions of some City supporters during the minute's silence before today's game.
"The club sincerely apologises to all those connected with Liverpool Football Club."
Oliver cut the tribute short as a result of what happened.
After the match, City manager Pep Guardiola said: "This is not Manchester City. We are close to Liverpool club for the tragedy that happened years ago. We are alongside them ... [The boos] doesn't represent what we are."
Liverpool manager Jurgen Klopp said: "We never thought this was Man City. It was some people who didn't understand the situation and that's not nice. It felt really wrong in that moment but that had nothing to do with City and of course we accept that."
Liverpool won the match 3-2 to reach their first FA Cup final since 2012, while City last won the competition in 2019.