Manchester City's second home defeat in four days ended in acrimony on Wednesday night as Steven Gerrard and Roberto Mancini argued in the tunnel. The Italian had asserted that Glen Johnson should have been sent off in the closing moments of the Carling Cup semi-final.

Gerrard, the Liverpool captain whose first-half penalty secured a 1-0 first-leg lead for Kenny Dalglish's team, accused the City manager of double standards, for demanding a red card for Johnson having condemned Wayne Rooney for doing likewise before Vincent Kompany was sent off in the FA Cup defeat by Manchester United on Sunday.

Kompany's absence was sorely felt by City as his replacement, Stefan Savic, conceded the decisive penalty with a foul on Daniel Agger. But it was Johnson's late challenge on Joleon Lescott – for which no free-kick was awarded – that provided controversy.

The Liverpool defender won the ball with both feet off the floor, leaving the City manager aggrieved that the same letter-of-the-law interpretation that led Chris Foy to dismiss his captain on Sunday – and resulted in a four-game ban for Kompany – was not applied by Lee Mason.

Kompany, writing on Facebook before the game, had asked: "I wonder though if we are now going to see an unprecedented wave of red cards on match days because we sanction 'ifs' and 'maybes'?"

Gerrard denied Mancini's complaints that Johnson's tackle was more dangerous than the one committed on Nani by the City captain. "I don't think so. It was a clear winner of the tackle," said the Liverpool captain. "I'm surprised at Mancini. 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."

Gerrard aired his view directly to Mancini, who said: "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."

City, having gone unbeaten at home in 2011, have lost twice in cup competitions in four days, with Liverpool becoming the first away team to keep a clean sheet here this season. Dalglish, who said he did not see Johnson's challenge, said: "We gave two different performances in each half. In the first half we looked a lot more threatening but in the second, after getting the goal advantage, we just battened down the hatches. Not too many teams have come here and not had goals against them, so it's a fantastic effort by us.

"It wasn't the prettiest performance, but it didn't fall short in terms of desire or commitment in any shape or form. Once we got ourselves in front, we were determined not to lose it. We might have a slight advantage with the goal, but there will be nobody jumping through hoops at our place. We'll just be as professional as we can at our place."

Mancini bemoaned a lack of cutting edge from a City team who missed the injured David Silva and saw Mario Balotelli limp off with a suspected ankle injury after 39 minutes. The City manager said: "The first half we didn't play well. After six months that can happen. But in the second half Liverpool did not pass the middle of the pitch. We had chances but didn't score but we knew before the game it would be difficult.

"It is difficult because we were without three or four players. The result is not right. For me it was a draw. We played two difficult games. I knew that was going to happen. January is going to be an important month but I think in both games we didn't deserve to lose. The second leg is going to be difficult. Liverpool are favourites because they won 1-0 away."

Gerrard echoed Dalglish's view that the semi-final was finely poised for the second leg, at Anfield on 25 January. "It is good to be back. I feel like a footballer again," said Gerrard of his second successive start. "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."