After their dramatic Barclays Premier League victory last term, City and Mancini began this term with high expectations but they have failed to build on that achievement.
Manchester United reclaimed the domestic title at a canter and City slumped out of the Champions League at the group stage.
That has left them chasing the consolation prizes of second place and the FA Cup, for which they play Wigan in the final at Wembley this weekend.
Mancini said: "When you start the season you want to win the best trophies or the most trophies but sometimes it is not possible.
"I think we did a good season but not like last season.
"I think the FA Cup is the second trophy in England after the Premier League. It is an important trophy for everyone. To play a final at Wembley is fantastic.
"For us it is the second final in two years. We have the chance to get another cup and we want to do a good job. We know it will be difficult."