Some pundits have suggested Mancini could face the sack if City, whose Barclays Premier League title defence is faltering, are knocked out of the FA Cup by Leeds this weekend.
Former Manchester City and Leeds defender Danny Mills has even said a successor could be appointed by Thursday if Mancini's last realistic hope of winning silverware is ended.
Mancini, speaking at a press conference to preview the fifth-round tie, said: "We started our project three years ago.
"In three years we are always on the top - we fight for the title, we have 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."
Mancini, who succeeded Mark Hughes in December 2009, ended City's 35-year trophy drought by guiding them to FA Cup success in 2011.
He followed that by overseeing a first title win in 44 years last May and then added an additional trophy in the Community Shield.
Yet last weekend's 3-1 loss at struggling Southampton, after which Manchester United extended their lead at top of the table to 12 points, has brought renewed speculation over Mancini's position.
When told he had been criticised by "former City players", Mancini responded by saying they were "probably the players that won a lot of trophies in the history".