The Liverpool skipper was annoyed that Mancini had been demanding a red card for Glen Johnson's two-footed tackle late in the game, as Vincent Kompany had been in the Manchester derby at the weekend.
"It was a clear winner of the tackle," said Gerrard. "He had a go at Wayne Rooney last week for trying to get one of his players sent off. Now he's trying to get one of our players in trouble. I don't think that's right."
Mancini responded: "It was worse, this tackle was worse. Johnson's tackle was worse than the one Vinny did against United. Everyone can see this. It was worse. Gerrard came to me and said, 'You said this.' Gerrard can say what he wants. No problem. The world is going down because people do not apologise. I make a mistake and I apologise. I say what I think and it is not important what Steven Gerrard and other players say."