The delighted Italian saw his side surge into a 2-0 lead with barely five minutes on the clock, but then have to survive a concerted fightback as Andy Carroll led an onslaught. City climbed into second place in the Barclays Premier League table, two points behind Manchester United having played two more games, as a result, although Mancini is not getting carried away.
He said: "I like Boxing Day. Last year, we won; this year, we won. I am happy with this first year, but it is my opinion that we need to improve again, we need to work."
He added: "Only if we do that can we arrive at the top and win something at the end of the season."
Asked to sum up his first year in charge at Eastlands, Mancini added: "(It has been) Fantastic because the Barclays Premier League is the best league at this moment in Europe and for me, it is an incredible experience."
Newcastle could hardly have got off to a worse start, nor City a better one, as the visitors found themselves 2-0 up in a breathless opening. Carlos Tevez fed Gareth Barry to give the visitors the lead after just 72 seconds, and then scored himself with just five minutes gone.
Carroll headed home is 11th goal of the season with 18 minutes remaining to set up a tense finish, but Tevez wrapped up the win with nine minutes remaining when his shot deflected off both Jose Enrique and Fabricio Coloccini and dropped inside the post.
The goals were Tevez's first since his transfer request was withdrawn and peace broke out at Eastlands, although Mancini was at pains to praise the whole team.
He said: "I am happy because Carlos scored two goals and I am happy for all the players because they played very well.
"They defended very well - it was difficult because they [Newcastle] played the long ball for Carroll and we fought for every ball against him because Carroll is a good player."