City claimed a narrow 1-0 victory against United at the Etihad Stadium in a fixture billed as a potential title decider.
The win allowed Mancini's team to go top of the table on goal difference, putting them in pole position to claim their first Premier League title, but the Italian insisted that City still have plenty to do.
"Newcastle will be our hardest game - harder than United," Mancini told reporters. "It is strange but it is like this.
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"They have had a fantastic season and are playing to get into the Champions League. Their manager is one of the best managers here and it will be a tough game.
"It is another Champions League final on Sunday. We have two - Newcastle and QPR. We have to keep a big concentration until May 13."
Mancini hoped that City's ascent back to top spot would not affect their performances in the final two games of the season.
Comfortable victories against Wolves, Norwich City and West Brom put City in a position to leapfrog United, their Manchester rivals having dropped points against Everton and Wigan Athletic.
"We have done nothing yet," Mancini reiterated. "We are at the top but we need to win two games.
"We need to play well and we need to score if we want to win. They will get six points.
"We are happy for the crowd but it is important our supporters do not think it is finished. We need to be very calm.
"We need to concentrate on the next game, work well, recover. The message is to keep calm, like one and two weeks ago. Nothing has changed."
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Mancini's relationship with Tevez seemed irreparable during the 28-year-old's mid-season spell away from the club but they now seem to have patched up their differences.
"Why not?" Mancini replied when asked if Tevez could stay. "He has a contract, he is a good player.
"But now our concentration should be on Newcastle."
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