The Italian admitted it was important for his side to record a win after an excellent performance against Manchester United last weekend ended in a last-minute 3-2 defeat.
"The performance against Manchester United was fantastic. We were disappointed for the result and finish," said Mancini.
"Today it was difficult because clearly after the defeat against United you need to restart quickly. We had a difficult game against Newcastle but I think the guys were really, really good.
"All the players played very well, if not it would have been difficult to beat Newcastle 3-1, and I think it could have been six or seven because we missed a lot of chances to score.
"At 2-1, when you are missing three or four chances like we did in the first half, if they had scored they would have opened the game. But after we were strong because we scored another goal and we had our chance."
Mancini restored Sergio Aguero and Carlos Tevez to the starting line-up, a strike partnership that has yielded 13 wins from 13 games, while Mario Balotelli was left out of the squad altogether.
Despite the Argentinian duo's impressive record as a starting pair, Mancini insisted he would still be rotating his strikers.
He said: "I think they are perfect because they play very well together but we have Edin Dzeko also and when he came in today he was important because he kept the ball - it was important."
On Balotelli, he added: "He was at home because he needs to work. If he deserves to play it is because he works well. If not he can stay on the bench like all the other players."
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