The situation could have been worse for City in the Premier League clash at the Etihad on Sunday had Sergio Aguero not scored 12 minutes from time to rescue a point.
"Last year we recovered eight points in six games so I don't know why it can't happen this year," said Mancini.
"They have to play in the FA Cup and the Champions League so the season is long - three months - and we are confident. It is enough to recover three or four points in three games.
"For us it is important to play the derby two or three points behind and we have time to recover these points. We didn't play like we had in the last month but we are confident.
"Two years ago Chelsea were nine points behind and when they went to play at Old Trafford two games from the end they were only two points behind.
"I don't think this is finished but probably now we have to win all the games but if not then 11 or 12 games. But in football this can happen sometimes."
Edin Dzeko put the hosts in front before strikes from Daniel Sturridge and Steven Gerrard turned the game in favour of Liverpool.
Mancini felt aggrieved that play had not stopped in the build-up to Sturridge's goal after Dzeko was challenged by Daniel Agger.
He said: "I think Liverpool played a good game. We conceded two goals, stupid goals for me.
"But before the first goal there was a big foul - if it had happened with us, probably there would have been a red card.
"Instead, the referee and linesman did not see anything. In the end, though, I think it was the right result."
Asked if he felt Liverpool should have put the ball out when Dzeko was left on the turf by Agger, Mancini said: "Probably, because after this foul I think there were several seconds (before the goal).
"I think so, but this can happen. I think it was a foul and should have been a yellow card. The rules are the same for everyone always."