City were pegged back in a difficult first half as Joe Hart saved brilliantly to deny Newcastle winger Hatem Ben Arfa.
Mancini replaced Samir Nasri with Nigel De Jong after the break, allowing Yaya Touré to push further forward – and the former Barcelona midfielder scored a quick-fire double to seal a valuable three points for City and move the Eastlands outfit three points clear of United, who host Swansea on Sunday.
When asked if City have one hand on the Premier League trophy, Mancini replied: “I hope so. But I think it is not enough because we have another difficult game like today.
“It was difficult because Newcastle are a good team. I think we deserved to win this game because we had a lot of chances. But it was a difficult game.
“In the second half after the Yaya Touré goal we had three or four more incredible chances.
“The pressure is not important. What is important is at this moment we have 86 points.
“The Manchester United result is not important now. We have another game and that all depends on the other team. I will be feeling confident after Queens Park Rangers.”
Touré put the visitors ahead after exchanging passes with Sergio Aguero and curling home his finish from 20 yards in the 70th minute.
The 28-year-old doubled City’s advantage from close-range on the stroke of full-time but Touré urged his team-mates not to underestimate relegation battlers Queens Park Rangers in their final game next Sunday.
“We have only one game to go but we have to be careful because Queens Park Rangers are fighting to stay in the Premier League,” Touré added.
“It’s going to be tough but we are one step closer to taking the title. We have to continue to work hard until the final minute of the season.”
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