Nigel de Jong’s second-ever City goal and Edin Dzeko’s 15th of the campaign twice gave the Blues hopes of the final as they battled to wipe out Liverpool’s 1-0 first-leg lead.
But a hotly-disputed penalty from Steven Gerrard, whose spot kick decided the Etihad tie, and former Blue Craig Bellamy squeezed Liverpool through despite Joe Hart’s heroics.
Liverpool’s penalty was extremely tough on Micah Richards, while Mancini was convinced that Charlie Adam should have been penalised for bringing down Dzeko earlier.
The Blues boss said: “Without the mistake on the penalty we would probably have won. It was no penalty. It should have been a penalty for us on Dzeko.
“The penalty for Dzeko was 100 per cent. For Micah, the ball hit his leg before it hit his arm.
It is impossible to consider a penalty like this and not consider one for Dzeko
“I’m not being critical of the referee, I’m just giving my opinion.”
Mancini added: “I’m happy with the performance. We’re disappointed with the result but we can do nothing now.
“After the penalty in the first leg we played well. Tonight was more difficult, Liverpool were strong, but we scored two goals when we needed two goals to go to the final.
“Their second goal was a stupid goal when you are winning 2-1 here in a semi-final and concede a goal like we did. If you score two goals here, you should be in the final.
“All competitions are important and we did everything we could to reach the final - now it’s finished and we have to think about the Barclays Premier League and the Europa League.”
Mancini replaced centre-back Stefan Savic with Sergio Aguero at half time. He said: “Savic is young and needs to improve, he makes mistakes like we all do. We needed another striker, that was the reason for the change.”
