Some pundits have suggested Mancini could face the sack if City, whose Premier League title defence is faltering, are knocked out of the FA Cup by Leeds this weekend.
Former 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".
It's a fairly simple equation for the owners, who have to balance stability, and what they expect to be achieved with £1bn in a league where nobody else could afford even a quarter of that. I don't think they expect to be 12 points behind their considerably worse-off rivals for that kind of money. But the devil is in the detail, as ever. In football you will get beaten by weaker teams, you can have the best squad by a distance and come second, and a £50m player can be a flop. All you can do is minimise these risks with shrewd decision-making, fantastic man-management and coaching, and so on. Does Mancini look to the owners like someone who did everything right, and was unfortunate, or does he look like the wrong man for the job? We will find out one way or another in Summer I think. He deserves a couple more years to build something lasting, but if I were him I wouldn't keep harping on about things like how RVP is 'the difference' (when Mancini spent over £20m on a player ten times in the last four years), how he needs to rebuild in the summer (when he has an embarrassment of riches that aren't playing to their potential under his management), or how everything is 'difficult' for City. That would p**s me off if it were my billion that had just been spent.- big dave