Having fallen 15 points behind United at the top of the Barclays Premier League with just nine games remaining, City's championship defence appears all but over.
But with the FA Cup still to play for, and the likes of Chelsea and Tottenham not out of the race for second, Mancini is determined to finish the campaign strongly.
The Italian said: "I think when you are a top team and you have good players, you should be very strong when you win or lose. This doesn't change.
"Also, when you can't win a title you can have other situations that you can improve.
"For this reason it is very important to do our best in the next nine games.
"We have the FA Cup and we have to get second position.
"I am sure Chelsea or Tottenham want to take second. We need to do our best for this reason, we want to stay there.
"If we take second position and have a chance to win the FA Cup - I think in the end, with all the problems we have had this year, I think this could be a good season."