Sergio Aguero broke the deadlock after 10 minutes with a close-range finish before Javi Garcia’s header put the Citizens in charge ahead of the interval.
Newcastle, who have now lost six of their last seven games, did offer their supporters brief hope after Demba Ba beat Joe Hart.
But Yaya Touré finished in the area to wrap up three points in the 78th minute and keep City on the coattails of Manchester United.
“It was a response only in terms of the result,” Mancini told Sky Sports.
“We were disappointed for the result and finish. Today was difficult. We needed to start quickly.
“The guys today were really, really good.
“All the players played very well, it could have finished 6-1 or 7-1 because we missed a lot of chances.
“When you’re missing three or four chances like we did in the first half, if they score, they open the game.”
Mancini also insisted Mario Balotelli remains part of his plans at City after leaving the Italy international out of his matchday squad.
“Yes [Balotelli has a future at City], why not? He was at home because he needs to work. If he works well he plays, if not, he stays on the bench.”
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