There have been calls for Mancini's dismissal after a disappointing season.
Mancini said: "In the last 18 months since United won the Premier title, there were seven trophies to play for and City won three of those.
"If I didn't win for two or three years I would say, 'I don't want to stay'. I just couldn't continue to stay.
"But I think that what we did in the last two years is important for the club.
"This year we still have two chances to win trophies - the league title and the FA Cup."