It has been suggested the Italian could be sacked if City are beaten in the fifth round of the cup by Championship Leeds on Sunday.
Speculation over Mancini's future at the Etihad Stadium - a recurring issue - has resurfaced after City fell 12 points behind Manchester United at the top of the Barclays Premier League last weekend.
With just 12 games remaining, City's hopes of retaining the title are now slim and the cup is their most realistic route to silverware.
Former City defender Danny Mills has even said Mancini could be removed early next week and a successor appointed by Thursday if Leeds pull off a shock win.
Mancini said: "We started our project three years ago. In three years we are always on the top - we fight for the title, we won three trophies, we have the chance to win more this year.
"All the people who talk about this don't understand football.
"Because if Manchester City should sack me, the other 20 teams in the Premier League should be without a manager."