"We were disappointed to lose to Everton," added Mancini. "And it was important that we had a victory at Newcastle, where it is difficult to win.
"The season is very long and we need to improve. We must continue to do this."
City also lost at home to Arsenal and dropped points in drawn games against Blackburn, Manchester United and Birmingham.
The victory at Newcastle started a sequence of four games in 11 days for City over the Christmas and New Year period.
"For me it is incredible," added Mancini of the fixture congestion. "It is an important period and we want to always try to win."
City led 2-0 after five minutes of their match at Newcastle - with Magpies keeper Tim Krul at fault for the first goal and midfielder Cheik Tiote giving away possession in the build up to the second.
"I do not think they were generous," said Mancini of the Newcastle errors. "It was a very difficult game because Newcastle are a strong team.
"We won because we played well and after we scored twice we fought for every ball. It was important to work very well on Newcastle striker Andy Carroll - every long ball for him was difficult.
"It is difficult to deal with him because in the area he is fantastic but today we defended very well."
Tevez scored twice and has now found the net 12 times in the Premier League this season.
"I'm happy because Carlos scored two goals," added the City boss. "But we won this game only because of all the players very well, especially James Milner, who for me played a fantastic game."
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