The delighted Italian saw his side surge into a 2-0 lead at St James' Park 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 Premier League table, two points behind arch-rivals Manchester United having played two more games, as a result, although Mancini is not getting carried away just yet.
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.
"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: "Fantastic because the 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.
Keeper Tim Krul was the villain for the opener when his ill-judged pass to Joey Barton was picked off by Carlos Tevez, who played in Gareth Barry to open the scoring with just 72 seconds on the clock.
The home side were carved apart once again with five minutes gone with Tevez this time setting up former Magpies favourite James Milner to cross and then arriving in the middle to guide his driven cross high into the net.
Newcastle, who had already lost three Premier League home games this season, might have crumbled, but to their credit, they worked their way back into the game despite repeatedly finding themselves at full-stretch.
They finally got their reward 18 minutes from time when Andy Carroll headed home Barton's corner, but their hopes of a fightback were dashed when Tevez fired home a third with the help of deflections off both Jose Enrique and Fabricio Coloccini with nine minutes remaining.
The goals were Tevez's first since his transfer request was withdrawn and peace broke out at Eastlands, although Mancini was at pains to praise the whole team.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."
Opposite number Alan Pardew was left to reflect upon what might have been after a home defeat to go with those suffered against Blackpool, Stoke and Blackburn.
He said: "Some of the opposition we have had, you would expect us to win, but I think most people would have come here hoping to win rather than expecting to win because they are a very good side.
"I am disappointed that we have lost, but on a technical level, the first phase cost us the game. If we started the game as we should at home, we could have got a win."