City reduced United's lead to a still formidable 12 points with a 1-0 success at relegation-threatened Aston Villa on Monday night courtesy of Carlos Tevez's first half goal in stoppage time.
But City manager Mancini acknowledges a failure to overcome other struggling opponents this season, despite carving out plenty of chances, has been a key factor in their downfall.
He said: "At Southampton, we played very well and we lost (3-1). We had other games like the one at Villa - against QPR and West Ham - where we missed four or five incredible chances.
"Even in the Villa game, we had other chances to close out the match rather than winning 1-0. It has been our problem this year and has cost us points.
"We have a lot of chances in every game that we are missing. This is the difference at this moment (from last season)."
Mancini concedes City may need to win their remaining 10 games to have any hope of overhauling United.
But he will be without midfielder Jack Rodwell for the first part of that demanding task after he suffered another setback to his long term hamstring problem at Villa Park.
Mancini confirmed Rodwell will be sidelined for "three to four weeks" after being substituted during the first half. He said: "Jack was distraught in the changing room. I am very sorry because he is such a promising young player.
"He needs to improve but he had played very well against Chelsea in the previous game and had been playing very well at Villa."
