City crashed out of Europe's premier club competition on Wednesday, with a 1-1 draw at the Etihad Stadium against Real Madrid sealing their fate.
The reigning Premier League champions have failed to secure a continental success this season, with five fixtures producing just three points.
Mancini's men have now tumbled out at the group stage in successive seasons, with the Italian yet to find a formula that works when pitched against the best in the business.
He is, however, of the opinion that owner Sheikh Mansour will not be following the lead of axe-wielding Chelsea supremo Roman Abramovich, with City prepared to be patient in their quest to claim major honours at home and abroad.
Asked after the Real defeat if he feared for his future, Mancini said: "No. I don't fear this. Why?
"We still have the Premier League and the FA Cup.
"If we think we can win the Champions League after two years we are crazy."