City are facing the very real possibility of premature elimination from the competition for a second successive season after collecting just one point from their opening three Group D games.
They now host the Ajax side that beat them 3-1 in Amsterdam a fortnight ago looking for a victory to at least breathe some life into their misfiring campaign.
The task is made harder by a host of injuries with Joleon Lescott and James Milner the latest additions to a casualty list that includes Micah Richards, David Silva, Maicon and Jack Rodwell.
But manager Mancini said: "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 on the pitch.
"This is the last chance for us."
Mancini faced criticism over his tactics after the loss in Holland and he is struggling to improve his underwhelming overall record in the competition.
The former Inter Milan boss has never taken a team beyond the quarter-finals but he insists there is no secret to managing in the Champions League.
He just feels his current team are collectively inexperienced at this level.
The 47-year-old said: "For me, it is the same, 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."