The Italian says he has no interest in his title rivals' much-hyped clash with Liverpool as he prepares for a testing trip to Arsenal on the same day.
Mancini's champions trail United by seven points at the top of the Premier League, a gap that could be 10 by the time City kick-off at the Emirates Stadium.
With a number of key players missing - including Yaya Toure, Sergio Aguero and Samir Nasri - Mancini wants to focus only on his own team and not the pressures of the title race.
He said: "We should go our way. We can't think about United or other teams.
"We don't see the table in this moment but at the end of February.
"Also it is difficult because we are missing important players but we want to do a good job on Sunday."
The Toure brothers, midfield star Yaya and defender Kolo, are preparing for the African Nations Cup with Ivory Coast, striker Aguero has a hamstring injury and former Arsenal playmaker Nasri is suspended.
Defender Aleksandar Kolarov is back in contention but Maicon, Micah Richards and Jack Rodwell are still sidelined.
Mancini said: "We can do nothing - Yaya is in South Africa but the problem is we are missing three or four important players, Samir, Sergio and the others.
"But I think if we work hard we can do well.
"Yes, we have had a lot of injuries this year. Last year we were really lucky, this year maybe not.
"We have had important players injured but this is football. We need to work, we need to work with players we have.
"We should take one or two young players because we have 16 and we hope we can recover injured players for next week."
Mancini is not concerning himself with United because he feels there is plenty of time to overhaul the deficit.
With City having memorably recovered from eight points down with six games remaining to win the title last season, he knows there is no need to panic yet.
He said: "I don't think we deserve to be seven points behind but now we can do nothing, only start to win.
"We have a difficult game now, because we play against Arsenal, but the season is long and is very difficult.
"We have another 17 games. I think we can recover these points."
City hope Aguero will be fit to return for next week's clash with Fulham.
The Argentinian, last season's top scorer with 30 goals, tore a hamstring in the New Year's Day win over Stoke.
Edin Dzeko and Carlos Tevez are likely to continue up front in his absence although Mario Balotelli is back in contention after overcoming a virus and scoring twice for the under-21s on Monday.
Alongside Aguero, Dzeko is the team's top scorer this term with 10 but despite scoring three in his last three starts, is still to shake off a reputation for performing better as an impact substitute.
Mancini said: "It is important Edin plays like against Norwich and against Stoke.
"If he play likes like he did against these two teams he could be important.
"I don't think there is one player that is happy to stay on the bench but we can play only with 11 players and someone should go on the bench sometimes.
"If Edin continues to score, I don't think we can have a problem."