City returned to the top of the table following Sunday's 1-0 victory at Aston Villa after being deposed for 24 hours by near neighbours United.
On his side's title bid, Mancini said: "We've 13 games from now until the end (of the season), and we know if we want to win the league we have to win 11 or 12, if possible."
After winning one of their previous six away games, the win at Villa was a vital triumph for Mancini and his players that came courtesy of Joleon Lescott's third goal of the season in the 63rd minute.
After a particularly troubled January, Mancini is naturally hoping the worst is behind his team, particularly as City will be back to full strength for their next league game at home to Blackburn in 12 days' time.
With Kolo and Yaya Toure back from African Nations Cup duty and Mario Balotelli having now completed a four-match ban, Mancini said: "We know December and January were difficult months.
"We had players injured, suspended or away. All these reasons.
"But now we are in February and we are still on top.
"Next week we will have all the players, which is very important for us.
"But to stay on top with Manchester United and Tottenham shows we are very strong."