City beat Arsenal 2-0 at the Emirates Stadium in the Premier League on Sunday - their first win away to the Gunners since 1975 - to stay seven points adrift of United, who had seen off Liverpool 2-1 earlier in the day.
Mancini admitted United are currently in good form but remains adamant the reigning champions can close the gap on their local rivals and retain their title.
"United are a really strong team," he said. "In this moment, they play very well. But the season is long. It's important for us to be there, close with them, and we will arrive the moment they lose points.
"We're under pressure maybe before, but seven, eight or nine points, everything can change at the moment. We have the derby on April 6 and we need to arrive there with five or four points behind, it is okay."
City were in the driving seat early on in north London when Arsenal defender Laurent Koscielny was dismissed after just 10 minutes for hauling Edin Dzeko to the ground inside the area.
The Bosnia striker saw his resulting penalty saved but atoned for the miss by tapping home City's second goal after a tremendous James Milner effort had broken the deadlock.
Captain Vincent Kompany was dismissed towards the end of the game to blemish a very good result for City but Mancini reckons he will not have to do without the Belgium international as Mike Dean's decision will be overturned.
"We will do an appeal and I think we can win, because it's easy, it is correct," he said. "But we have a problem because we're missing a lot of players. Now we are losing him for three games, but I don't think we should."
If any appeal is lodged and is ultimately rejected, City would be without their skipper for the Premier League matches with Fulham and QPR and an FA Cup fourth-round tie against either Crystal Palace or Stoke.
There is also the possibility that an extra game could be added to the ban if the appeal is deemed to be a frivolous one, which would mean Kompany would miss the visit of Liverpool on February 3.
Kompany took to Twitter to defend the challenge, but stopped short of criticising Dean's decision to send him off.
"First. Massive congrats to our team and fans, great game! Also. No grudges against the referee, I understand the difficulty of the job," he tweeted.
"About the tackle: If the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable.
"Ultimately I'm a defender: Appeal may work or not. I will never pull out of a challenge, as much as I will never intend to injury a player."