Mancini felt a Glen Johnson tackle on Joleon Lescott should have been punished for being two-footed, claiming it was worse than the challenge that resulted in a red card for Vincent Kompany in Sunday's FA Cup tie with Manchester United.
But Gerrard disagreed and made his feelings known to Mancini.
While Mancini was waiting to talk to a gathering of journalists, Gerrard approached him.
The Liverpool captain, pointing a finger at the City boss then waving an imaginary card, said to Mancini: "You say to the press that Wayne Rooney tried to get Kompany sent off - and you try to get Johnson sent off."
While listening to him, Mancini said "I say what I want" and "yes, yes" but what he was agreeing with was unclear.
Gerrard then shook his head, turned around and walked away, then Mancini shouted back at him but what he actually said cannot be understood.
"Gerrard came to me and said I said something," commented the Italian, who clashed twice with the England international.
"Steven Gerrard can say what he wants. I said what I think. That is what I am used to doing. It is not important what Gerrard or the other players have said."
Mancini claimed that his anger was directed at the inconsistency of refereeing decisions more than at Liverpool defender Johnson.
"I said something [after the tackle]," he said. "It was not for Johnson. It is for the tackle. This tackle was worse than Vinny's. Everyone can see it."
When asked if he agreed with Mancini's view on Johnson's challenge on Lescott, Gerrard told BBC Sport: "I don't think so. It was a clear winner of a tackle."
Phil McNultyChief football writer
“There's a real sense of injustice among the Man City fans at Etihad Stadium. There wasn't much difference between that tackle from Glen Johnson and Vincent Kompany's on Nani on Sunday”
The Liverpool midfielder, whose penalty resulted in the only goal of the game, went on to claim Mancini was guilty of hypocrisy.
"He was talking about Wayne Rooney trying to get his player [Kompany] sent off and now he's trying to get one of ours into trouble," he said. "I don't think that works."
Liverpool manager Kenny Dalglish maintained that he had not seen the incident.
Kompany, who missed the game with Liverpool after receiving a four-match ban for his tackle on Nani, will also sit out the league games against Wigan and Tottenham as well as the return leg with Liverpool at Anfield on 25 January.
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