Carlos Tevez's first-half goal gave last year's champions a 1-0 win at Aston Villa on Monday night, closing the gap to leaders Manchester United back down to 12 points, though the Italian admits that it would take a perfect run-in to win a second triumph in as many years.
"We need to win all 10 matches," Mancini told reporters after the game.
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"We had a few games like QPR, West Ham and Chelsea away where we deserved to win but missed two or three chances to score but sometimes it's enough to win 1-0 like tonight, to fight for every ball, because now the result is very important."
Mancini also offered updates on injuries, revealing that Jack Rodwell is likely to be out for around four weeks after limping off the pitch with a hamstring injury, while the club will try to make sure that Sergio Aguero, whose knee injury prevented him from featuring against Villa, is fit for their clash with Everton on March 16.
"We are very sorry for Jack, he is unlucky," the Italian lamented. "It's a hamstring injury. Maybe after the international break [he will be back].
"He's a good player. He's young and needs to improve but he played very well against Chelsea and was playing well tonight.
"Aguero fell on his knee early on in training yesterday. If possible we want him to play against Everton [but he will not be ready for Barnsley in the FA Cup]."