Mancini believes their FA Cup win over Leeds United can spark his team into life.
"It is possible we could be 15 points behind by the time we face Chelsea next Sunday, but I think we should always be confident in ourselves," Mancini said.
"There was a stage where we lost seven points in three games and that can happen to other teams as well.
"So, even when we're 12 points behind at this moment, we should believe it can be done. At this moment, United deserve to stay there because they have been better than us and scored more goals, but this win against Leeds can influence what we do for the rest of the season and spark us into life.
"We have been unlucky with injuries this season, but Gareth Barry should be ready for Chelsea, and we hope we have Vinny Kompany for that one as well. We will see tomorrow or Tuesday about Javi Garcia, but I don't think it's big problem with him, either."