Mancini conceded defeat at Arsenal this weekend, coupled with a win for rivals Manchester United over QPR, would all but condemn City to the runners-up spot.
Yet the Italian is determined that will not happen and, with seven games remaining, believes the five-point gap to United can be closed.
Mancini, whose side were overtaken by United in March after five months at the top, said: "I can say I am proud of what the players have done in this championship. We were on the top for a long time and we have been fighting with United until now.
"I think we have improved as a team, in the Premier League title. Maybe we did some mistakes in the Europa League, and also the Champions League - but with 10 points you (usually) go through.
"I think we have improved a lot as a team but it is not finished now. I don't believe this championship is finished. If they [United] win all their games, congratulations they deserved to win the title.
"But seven games from the end I think anything can happen. We lost four points in two games. It is possible to happen to them."
City's bid for a first title in 44 years stuttered in March as they were beaten at Swansea and held to frustrating draws by Stoke and Sunderland.
Being in a position to challenge is not one City are familiar with and the season could be taking its toll on players, but Mancini is not looking for excuses.
He said: "After seven months it could be that we have some players tired but it is not only us. The other teams have tired players. In this moment it is important to be strong."