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."