Roberto Mancini criticised the decision-making of referee Phil Dowd after Manchester City were knocked out in the Carling Cup semi-finals.
City drew 2-2 with Liverpool in the second leg but the Reds went through 3-2 on aggregate, thanks in part to Steven Gerrard's penalty.
Dowd awarded the spot-kick after Micah Richards blocked a shot and the ball deflected up onto his hand.
"It was impossible that it was a penalty," said City manager Mancini.
"Micah can't cut off his arm because the ball touched his leg before. It's impossible to concede a penalty like this and not give one with Edin Dzeko [when he went down in the box under a challenge from Liverpool midfielder Charlie Adam].
"I am 200% sure it [Dzeko incident] was a penalty. We were very unlucky for this moment with the referee."
He added: "Without the first penalty we would have won the game. It was not a penalty for Liverpool."
Richards later wrote on Twitter: "Not happy! How can I stop it hitting my hand if it hits my foot first! #badday"
Manchester City began with an unfamiliar defensive system, as Mancini employed three centre-backs, with Stefan Savic flanked by Joleon Lescott and Micah Richards.
A brilliant strike from Nigel de Jong put them ahead but Liverpool equalised when Gerrard scored from the spot after Richards' diving block on Daniel Agger's shot.
With the score at 1-1 at half-time but City trailing on aggregate, Mancini replaced Savic - who had endured a difficult first 45 minutes - and changed to a more familiar 4-4-2 formation.
But the Italian said he had no regrets about the tactics he employed.
"I'm happy with the performance because when you come here and score two goals against a team like Liverpool you should do a good performance but we made some mistakes," he commented.
"Savic is young, he needs to improve but he can make some mistakes like me and the other players.
"But we changed Savic after the first half because we were 1-1 and we needed to put another striker on the pitch, only for this reason."