Although United go into the most eagerly-awaited derby in years in winning form, while City lost at Everton on Saturday, Mancini is hopeful City can raise their game the triumph over their local rivals.
"We are meeting a big team but if we play well, I think we will go to the final," he said.
"We have two games and it is important that we play with concentration."
Mancini has previously spoken of his desire to banish the banner at Old Trafford which serves as a reminder of City's lack of silverware in recent years - their trophy drought stretches back to the 1976 League Cup final win over Newcastle - and the Italian clearly likes the idea of picking up a cup in his first couple of months as a manager in England.
However, he is also a pragmatist and if the harsh manner of Mark Hughes' dismissal taught him anything, it is probably that unless City make the Champions League spots this term - as demanded by owner Sheikh Mansour - he is likely to be out of the door whether he has won the Blues a trophy or not.
"We want to win the Carling or FA Cup, but we must finish in the top four," he said, before adding: "Yes", when asked if that was the priority.