City beat Stoke 3-0 at the Etihad Stadium on Wednesday night to stay two points clear of second-placed Manchester United and ensure an unbeaten home record in 2011.
Sergio Aguero's double either side of a long-range effort from Adam Johnson made the difference and Mancini – himself celebrating two years in charge of City – is delighted with the progress his side have made.
“I'm happy for our supporters that we are top at Christmas,” Mancini said. “They can have a good Christmas day but the important thing is to be there at the end of the season.
“Now is a difficult moment, we need to work more and believe in ourselves. Until now we have dominated this championship and for this reason we will work until the end.
“I'm happy. I'm feeling good after two years here. We are working very well and are at the top of the Barclays Premier League.
“It's important that we can continue to win at home. Being unbeaten at home this year is a good record but it's not that important.
“We are playing very well at the moment but sometimes it's not enough, like against Chelsea. The Barclays Premier League is very hard, it's very difficult.”
Stoke posed little trouble for City but Mancini praised his side for their patience in breaking down Tony Pulis' side, who set up with nine men behind the ball for most of the match.
“It's never easy,” Mancini added. “In the first 30 minutes it was difficult to find a goal but we produced a good performance. I think that all the players played very well.
“Sergio scored the first goal, which was very important as Stoke put all their players behind the ball.”