Manchester United, boosted by the goals of Robin van Persie, have romped to the Premier League title, and City are a huge 13 points adrift of their fierce rivals following Saturday's goalless draw at Swansea.
While Mancini is happy with a trip to Wembley and the runners-up spot, it will not make up for failing to defend their league crown.
When asked if he would be content with a second place finish, the Italian said: "I am not satisfied as I wanted to win the Premier League, but now we cannot do anything about that, we cannot change it.
"But in the end we we are in the cup final and we are in second position, so we can be satisfied. But when you start the season you want to win (the league)."
He added: "We hope we can win the cup but it won't be easy. Wigan are in good form and they won away (this weekend). It will be hard."