Ahead of the derby at Eastlands on Wednesday night, the Italian boss has reiterated that Chelsea will retain the title.
Mancini said: "I think Chelsea will win the Premier League as they are better than the other teams.
"But all the other sides that are near them can try because the season is long and difficult. We must play a lot of games.
"I think we can have a chance. We must take it game to game. For the moment we must only think of United."
United, however, secured their passage to Wembley thanks to a stoppage time winner from Wayne Rooney in the second leg.
He said: "A victory before you play United is important for the players and for all of us. They know now we are a strong team. The situation has changed.
"We have respect for them, we have respect for Fergie (Sir Alex Ferguson) because he is the top manager in the world. But we are getting better. It will be a good game.
"In the last three of four derbies City have played at the same level as United but have lost late in the game. This season we are a different team.
"They are a strong team who are ready to play until the last second. They won against Wolves like that. They have a strong mentality because they have won a lot of trophies."