For the second season in succession, City have no chance of making the Champions League last 16 after a record of three draws and two defeats left them bottom of Group D in the continent's premier competition with just three points.
On Tuesday, they go to German champions Borussia Dortmund who, along with Real Madrid, have already qualified for the knockout rounds leaving City and Ajax to aim for a Europa League place instead.
City must beat Dortmund and hope that Jose Mourinho's Real can prevent Ajax from a victory if they want to keep their European ambitions alive.
"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, who is not worried about his team lacking motivation without advancing in the Champions League.
"There is the Premier League, and the Europa League if we can go in it, and also the FA Cup. The season is long and it is important."
Mancini is also hoping his team can finally rediscover their killer instinct.
"We played very well at Chelsea and didn't win. We played well in the second half at Wigan. We are in good form at the moment," said the Italian.
"But we're not 100 per cent, because we are missing the goals from our strikers that they scored last season."
Mancini, who was booed by City fans for taking off top scorer Carlos Tevez in Saturday's 1-1 draw at home to Everton, will not have his assistant David Platt with him on the sidelines on Tuesday.
Platt was suspended by UEFA for two matches after improper conduct following his dismissal last time out against Real Madrid.
Borussia Dortmund have a number of injury concerns for the game.
Dortmund are already assured of first place in Group D ahead of Real Madrid, meaning Borussia coach Juergen Klopp can rest some players.
And a number of them need the break.
Neven Subotic was taken off during Dortmund's 1-1 weekend draw with Bayern Munich with a groin injury while captain Sebastian Kehl was out with a knee problem.
Sven Bender played despite not being 100 percent fit.
"Neven is a beast so I hope it's nothing serious. And you have to be impressed with how Sven Bender played," said Klopp after the Bayern match.
"I am happy that we already qualified for the Round of 16. We will have to see who we can send out onto the pitch. This phase is pretty tough for everyone."
Source: AFP