The City boss watched his side come back from 3-1 down to earn a 3-3 draw with Sunderland at the Etihad Stadium on Saturday, closing the gap to leaders United to two points.
United can move five points clear of their local rivals with victory at Blackburn Rovers on Monday night – but with the two sides set to meet at Eastlands on 30 April, Mancini is confident his side will keep pace with Sir Alex Ferguson’s men.
“It will be hard to win the Premier League now, but it is possible Manchester United will drop points too, in the games that remain,” said Mancini after Saturday’s game.
“We did well to come back the way we did, but we didn’t play well for most of this game.
“What we needed to do was play the way we did in the last 15 minutes – but at the start of this game – it was a strange match because it is very unusual for us to concede three goals at home.”
Mancini admitted his squad were dejected after the draw at Eastlands and was not impressed by Mario Balotelli’s display, despite the striker netting two of City’s goals.
“The players are disappointed and a little down, but only for this moment because I think United will only draw on Monday and if that happens, we’ll still only be three points behind,” he said.
“Mario [Balotelli] didn’t have a good game today in my opinion. In games like this we need the strikers to be the difference – not only in the final few minutes.”
“It is important we go into the Manchester derby at the end of the month only one or two points behind – if we are, we still have a very good chance – but we must recover two or three points in the games in-between.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news