Mancini has regularly cited the failure of his forwards to match the standards of last season as one of the reasons for the champions' faltering title defence.
City have found the net 50 times in their 27 league games to date, 19 behind their tally at the same stage last season and 18 less than United this term, although they have played a game more.
It is an issue City are expected to address in the summer but Mancini does not necessarily need an abundance of goals to get back into the title race.
The Italian said: "I hope that we can win the next 11 games 1-0 if it is possible because 1-0 is enough if you don't concede a goal.
"But it is impossible that you don't concede a goal every game.
"It is clear, if we are missing 15 or 16 goals now from last year, it is too much because 10 goals are probably six or seven points.
"This is the difference."
One of City's strikers, Carlos Tevez, has also set his sights on victory in every game to apply maximum pressure to United.
Tevez has scored 11 times this season including a superb long-strike to settle a tight contest with Chelsea last weekend.
The former United forward told the club's website: "I think that what we have left is 11 cup finals.
"There is not long between now and the rest of the season and we must win - we have to win.
"We're still in the race, we know we can still catch United.
"If we can get three points from every match and hope that United slip up here and there, we can maybe start to put some pressure on them.
"We would be fooling ourselves if we thought it was going to be easy.
"It will be very tough, but by picking up the points we will be fighting, believe me we will be fighting and while it is still mathematically possible, we will be going for it."
City's 2-0 win over Chelsea eased fears they might be dragged back into a battle for second place and restored confidence after a damaging loss at Southampton last month.
But Tevez also sees the Monday night trip to Villa Park to face another relegation-threatened side as fraught with danger and is anxious to ensure intensity does not slip.
He said: "It is very important that we stay strong - both mentally and physically - going into each of the remaining games.
"I think this is going to be a tough game.
"We know that Villa are battling against relegation and it's at their ground, so I think it's going to be treated like a final for them too, so that should make for a very entertaining match."
City will need a number of favours from elsewhere to pull off what would be an even more unlikely title triumph than last year's remarkable effort.
There has been little sign of it with United unbeaten in the league since November but Mancini has not forgotten where they slipped up last time.
He said: "It is difficult because last year nobody thought they could lose against Wigan or these games.
"When there are seven, eight, nine games to the end, it will be difficult because teams play for (to avoid) relegation, for the Europa League or the Champions League."
City are unlikely to be without captain Vincent Kompany as he continues to recover from calf problems but midfielder Gareth Barry is fit to face his former club after an ankle injury.
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