The reigning Premier League champions are 12 points behind leaders Manchester United but the Italian thinks Sunday's win can spark a comeback in the league
City's win in Sunday’s fifth round tie saw Sergio Aguero scored two goals and set up Carlos Tevez for another following Yaya Toure's opener, and the manager maintained that if his side can build on this performance the title race is not yet lost.
"I hope Sergio [Aguero] will be like this from now to the end of the season," he told reporters following the win.
"If he is and our other strikers continue to score until the end, then I think the championship is not finished.
"In Italy we say a game like this is a ‘brodino’ – a starter. I hope we start to win in the Premier League again."
The reigning champions have failed to win in their last three Premier League games, allowing United to open up a 12-point lead, but Mancini warns that this gap could disappear quickly.
"We should always be confident in ourselves, even when we’re 12 points behind at this moment. We lost seven points in three games and this can happen for any team," he continued.
"At this moment they deserve to stay there because they have been better than us and scored more goals than us. But now United play a lot of games."
The Italian also said he was hoping his side's injury problems were starting to clear up, adding:
"We are unlucky this year with injuries. We hope we can recover Vincent Kompany for the next game.
"I think Gareth Barry will be ready for Chelsea. Javier Garcia, we will see tomorrow or Tuesday, but I don’t think it’s big problem."
As for the FA Cup, he pointed out that Arsenal had demonstrated the challenge of the competition in their defeat to Blackburn on Saturday.
He explained: "The FA Cup is difficult. We saw that with Arsenal.
"Every team plays it like it’s a Champions League final. The FA Cup is an important trophy in England, because you should play 100 per cent if you want to win."