Gerrard's early penalty gave the visitors a 1-0 first leg lead to take back to Anfield but Wednesday's game was overshadowed by a late, two-footed challenge by Liverpool defender Glen Johnson on City's Joleon Lescott.
An angry Mancini claimed that the tackle, which went unpunished by referee Lee Mason, was worse than the offence committed by City's Vincent Kompany early in Sunday's FA Cup defeat by Manchester United, an incident which brought the defender a straight red card and a four-match suspension.
Mancini's claims were not appreciated by Gerrard, however, and the Italian and the England midfielder had a heated discussion about the incident in the tunnel after the game.
"No, I don't think so," said Gerrard when asked whether he felt Johnson should have been red-carded. "It was a clear winner of the tackle.
"I'm surprised at that (Mancini's comments). He had a go at Wayne Rooney last Sunday 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 works."
Mancini, though, had a different interpretation of the incident, one which television replays seemed to support.
"Johnson's tackle against Lescott, it was worse than the one Vinny did against United," said the City manager. "Everyone could see that.
"The world is going down because there are people in every job who make a mistake and do not apologise. I make a mistake and apologise.
"This tackle was worse. Gerrard came to me and said 'You said'...
"Steven Gerrard can say what he wants for me, no problem. I said what I think. I'm used to being like this. It's not important, Steven Gerrard or other players."
The late flashpoint marred a match in which City slumped to their fourth defeat in eight games.
Without brothers Kolo and Yaya Toure, on international duty with the Ivory Coast, plus the suspended Kompany and injured David Silva, City looked a shadow of the side that have built a three-point lead at the top of the Premier League.
"We played two difficult games," said Mancini of two home losses in four days followed a run of 30 unbeaten matches at Eastlands.
"I knew this before, January would be an important month for us because we have lost three or four important players and would probably have some problems. Both games, I didn't think we deserved to lose, but we lost."
Liverpool manager Kenny Dalglish was pleased with his team's display but refused to accept the return leg, in two weeks, would now be a much easier match for his side.
"In the second-half, after getting the goal advantage, we just battened down the hatches," he said.
"Not too many teams have come here and not had goals against, so it's a fantastic effort by us," the Liverpool great added.
"We might have a slight advantage with the goal, but there will be nobody jumping through hoops. We'll just be as professional as we can at our place.
"It's a fantastic performance by the team against a really good side, but we're not presuming that the job is done."
Dalglish, who claimed not to have seen the Johnson foul that incensed Mancini, was full of praise for match-winner Gerrard, looking back to near his best form after an injury-plagued year.
"Steven will get better every time he finishes a match," said Dalglish.
"He is gaining the benefit from it as well, so it?s great to see him back."
England midfielder Gerrard himself agreed, saying: "It is good to be back -- I feel like a footballer again.
I've had a difficult year and it's games like this I have missed and games like this I have worked to get back so hard for.
"We defended well from back to front. We were playing one of the big powers in world football. There is no way this game is over yet and it is set up nicely for the game at Anfield."