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.
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- Sir Alex Ferguson
- Barclays Premier League