The Italian has admitted his side will see their Champions League hopes completely extinguished should they fail to defeat Frank de Boer's side on Tuesday night
City have already suffered defeat to Frank de Boer's men this season and, having lost to Real Madrid and drawn at home against Borussia Dortmund, the English side are close to elimination.
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"We have this problem with some important players injured but when you have this problem, it is a time that all the players can put more [effort in] on the pitch,” Mancini told reporters.
"This is the last chance for us."
The Italian also reiterated his belief that his side are not currently equipped for European success, citing the fact that it is only the club’s second year in the competition.
"For me, [managing in Europe] is the same,” Mancini added. “But if I said we are ready to win the Champions League, this is not true. We need to improve.
"Probably there are other teams better than us in this competition because they have played every year in the Champions League."