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."
Mancini is expected to rest some of his squad for the midweek meeting with West Brom, but was quick to rule out any injury concerns over Yaya Toure and Carlos Tevez.
Toure was withdrawn at half-time at the Liberty Stadium while Tevez made a brief substitute appearance after being left on the bench.
After attributing Toure's substitution to tiredness, Mancini added: "We have rested Carlos as we need to give some players a rest with another important game on Tuesday."
While City have been the Premier League's form team in recent weeks, Swansea have been on a miserable winless run, which now stretches to seven games.
The stalemate with City was also the third game in which the Swans have failed to find the net, and they suffered the further blow of topscorer Michu picking up a hamstring injury which is set to end his season.
But manager Michael Laudrup is remaining positive, and believes one more win will be enough to secure the top-10 finish he has targeted since their Capital One Cup success.
He said: "I have to be pleased. We are still ninth with a game in hand and if we get one win in our last three games we will finish top 10, which would be huge."
He added: "This is not the first time we have talked about the final ball or our finishing after a game, but we will have to try and improve."
Source: Manchester City MAD