The Barclays Premier League champions, who headed to Newcastle trailing Manchester United by six points, ensured the gap did not grow by beating the Magpies 3-1.
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."
City took the lead with 10 minutes gone when, after a bright start by Newcastle, Yaya Toure split their defence with a pinpoint pass for Samir Nasri to square for Sergio Aguero to tap into an empty net.
They extended their lead six minutes before the break when Javi Garcia's header from a David Silva corner eluded Davide Santon on the line.
However, the Magpies responded after the break with Demba Ba's 51st-minute header dragging them back into the game, and strike-partner Papiss Cisse fired inches over on the turn two minutes later with the Magpies going for broke.
But victory was sealed with 12 minutes remaining as Toure slid home Pablo Zabaleta's cross to ended Newcastle's hopes.
Mancini was disappointed with a series of first-half chances which went begging, but satisfied with the end result.
He said: "I don't understand why we missed all those chances in the first half because when you come to play here, it's difficult because Newcastle are a really good team and they played very well.
"When you have six, seven, eight chances to score, you need to score more goals because if not, it can happen like in the second half when after they scored their goal, it changed everything."
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, 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."
Meanwhile, City striker Mario Balotelli was conspicuous by his absence on Tyneside having been left behind following his less than impressive display against United.
Mancini said: "He is not in good form at this moment and it was better for him that he continued to train and to train well. When he is in form, he will play.
"His form is not good - it's not good to play."