The Barclays Premier League champions beat the Magpies 3-1 and it was the perfect response to their 3-2 derby defeat last weekend, and Mancini was delighted with the application of his players.
He said: "It's important because when you come from a defeat - any defeat, but particularly against United - it's important to start to win quickly, and we started here, where I don't think a lot of teams can win."
However, asked what message the victory sent out to Sir Alex Ferguson and his players, Mancini added: "The message is only for Christmas on December 25.
"The season is long. He (Ferguson) knows football better than me. He knows that this championship is not finished when there are only three games to the end. Now that we have 24, 23 games to the end, it is open."
Opposite number Alan Pardew was left to reflect upon a sixth league defeat in seven games, but was able to take a series of positives from a spirited display.
He said: "I look at us and I have been in runs with other teams and I have played in some teams as well where you don't feel you can score, and that's a real worry, when you don't think you have got a goal in the team.
"But you have to say over the last three or four games, you can't say that about us. We look like we have got goals. We are just missing a bit of concentration, a little bit of resilience.
"At 2-1, we were really, really in a game there with a team who you couldn't say had played poorly. They were right at it today, Manchester City, so there are a lot of positives for us.
"Unfortunately, it's zero points and that's putting us under pressure now going into QPR, which we know here is a big game now."
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- Sir Alex Ferguson
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