City crashed out of the Europa League to Sporting Lisbon on away goals on Thursday after a 3-3 aggregate draw.
City now face Chelsea on Wednesday at the Etihad Stadium.
Mancini said: “If we have the same spirit as we had in the second half, we can win the next game against Chelsea.
“And I am confident for the Premier League, because we stayed on top for seven months and now we are in second position, one point behind. I am very confident we can win the title.
“I think that now it will be a good fight until the end of the season, because we have only the Premier League and we can put all of our strength into this. I think it will be good.”
