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."
City, despite producing a consistency most clubs would envy, have not been able to repeat the exhilarating football of last season.
There have been a number of reasons for that, starting with the obvious draining effect last year's dramatic success had.
Mancini hoped to freshen his squad up with high-quality summer recruits but failed to land all his prime targets, most notably Robin van Persie.
What they missed out on has been abundantly clear with the prolific Dutchman making a huge difference to United's side.
United began to edge into a decisive lead after winning the derby at the Etihad Stadium in December and City, who have suffered injuries to key players, have been unable to respond.
United's form has been relentless but City have failed to apply enough pressure and gradually slipped away.
Mancini said: "We are so disappointed because we can't win the title but until now I think United have been better than us.
"They probably deserve to stay on the top.
"But we know in football it is impossible to win the title every year. The second year is probably the most difficult."
Mancini, whose position has been the subject of recurring speculation, even claims it would not be a disaster if his side missed out on second, although he will not allow that to happen.
He said: "A disaster - no. But in football anything can happen if you don't play well, if you don't work hard.
"I don't think this can happen but we should pay attention."
City return to action for the first time since a damaging 2-0 loss at Everton a fortnight ago as Newcastle visit Eastlands this weekend.
Mancini has continued to bemoan his team's shortcomings - most notably a failure to convert goalscoring chances - but trusts and expects his players to respond.
He said: "They have my trust. This is not a problem but I think sometimes we should do more and more.
"In the end we shot 22 times at goal (at Everton) and didn't score.
"This is the problem we have had this year, but we didn't play well.
"We have Chelsea four points behind, Tottenham five points. For this reason it is important we keep going hard, working well."
Newcastle, who are through to the quarter-finals of the Europa League, also need to finish strongly to end any lingering fear of relegation.
Mancini said: "Newcastle changed three or four players in the January market and I think they improved their team.
"Also they also have a good manager and they are doing very well in the Europa League.
"Every time we play against Newcastle it is difficult because they have good players."
Captain Vincent Kompany, who irritated Mancini by playing for Belgium in midweek, looks set to return after an eight-week absence with a calf injury.
Kolo Toure, returning to prominence, has performed impressively in his place but with his contract due to expire at the end of the season his future remains uncertain.
Mancini said: "Every player wants to play every game and maybe for Kolo he thinks it could be difficult next year.
"If he thinks for him it is better to leave we can help him.
"Kolo is a positive guy and probably deserves to play. I can understand."
Striker Sergio Aguero is also fit after three games out with knee trouble.