Mancini refused to accept that his side may have to settle for second place, and also revealed that captain Vincent Kompany could return from injury within the next week or so.
"We have to keep on winning and see. This is football nothing is impossible. We know it will be difficult but we will keep on trying. For us it was important to stay 12 points behind United and for us the championship is not over," said Mancini.
"We are playing well. We had good chances and Aston Villa are a good team. It is strange that they are down there and for that reason I am happy with my team. We hope that maybe for the FA Cup [against Burnley on March 9] or Everton [March 16], Vincent Kompany will be back."
The Italian manager also lamented the luck of midfielder Jack Rodwell, who was stretchered off with a hamstring injury midway through the first half.
"Jack Rodwell is very unlucky, I was very happy with how he played against Chelsea and he has done his hamstring," Mancini added.
City's next match comes against Barnsley in the FA Cup before travelling to Liverpool to take on Everton in their next league game.