On a day that saw Everton complete a miraculous comeback and hold United to a 4-4 draw, City's win over Terry Connor's side had closed the gap at the top of the Premier League table to just three points.
Mancini – who had previously written off his players' title bid - insists his side has a 'chance', however, he believes that City have a harder run in than Sir Alex Ferguson's men.
City host United in the Manchester derby on April 30, in what could be the title decider. The Citizens then go on to play Newcastle and QPR, while the Red Devils take on Swansea and Sunderland.
"They have a bigger chance, more than us. I think we have difficult games," the Italian tactician told Sky Sports.
"I'm pleased with our form. For now until the end we have three games, United, Newcastle and QPR.
"United? After us their games aren't easy, but not as difficult as ours. I think we have another chance."
A win for Mancini's men on derby day will see his side reclaim top spot on goal difference. However, victory for United will see them extend their lead at the top of the league to six points, effectively sealing the title with two games remaining.