The English champions have a near-impossible task to qualify for the knockout stages of the Champions League but the Italian insists that a trophy win is still important
The Premier League title holders currently sit bottom of Group D with two points from four games and would need to beat Real Madrid and Borussia Dortmund to have any chance of qualifying for the next phase.
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"We don't have any chance to go through to the next stage but, like goalkeepers, football is strange," Mancini told reporters.
"We have two games and we want to be in the Europa League.
"Maybe when you play in February, March, April it can be a problem but if you can reach the final, the Europa League is an important trophy."
City would require results to go their way to progress in the Champions League even if they beat the Spanish and German champions and must overhaul Ajax, currently two points ahead of them, just to qualify for the Europa League.
Mancini's men featured in the competition last season after a similar third-place group finish but were knocked out on away goals by Portuguese side Sporting Lisbon.