Mancini's champions trail neighbours United by seven points at the top of the Premier League and the gap could be 10 by the time City kick-off at the Emirates Stadium.
But the Italian, who is without Yaya Toure, Sergio Aguero and Samir Nasri, urged his players to shut out their title rivals' much-hyped clash.
He said: "We should go our way. We can't think about United or other teams.
"Also it is difficult because we are missing important players but we want to do a good job on Sunday.
"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."
Edin Dzeko and Carlos Tevez are likely to continue up front in Aguero's 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."
Arsenal v Manchester City is live on Sky Sports 1 this Sunday. For more details click here