The reigning Premier League champions currently sit at the bottom of Group D after five matches and their European campaign will be over if they cannot overcome Borussia Dortmund at Signal-Iduna Park on Tuesday.
City needs to record three points, or at least a draw, and hope Ajax lose to Real Madrid in Spain if they are to finish third in the group and drop automatically into Europe's second tier competition after missing the boat for the Champions League knockout stage.
"We will try but we need to win in Dortmund and it will not be easy because Dortmund are in a good condition," said Mancini.
"There is the league, and the Europa League if we can go in it, and also the FA Cup. The season is long and it is important.
"We are disappointed we are out of the Champions League but I think we lost our qualification in the first games.
"I think we should also be lucky during the draw. The Champions League is always difficult but we took a worse group than last year."