The Dutch striker joined United from Arsenal for a reported 24 million pounds last August and his 14 goals in 20 league games have helped Sir Alex Ferguson's team open a seven-point Premier League lead over defending champions City.
"At the moment, he is the difference between us," Mancini told local media. "He has scored 14 Premier League goals and it is clear he has changed their situation.
"We were very close three or four months before he joined United. We were sure he was for us but it didn't happen.
"We wanted Van Persie because we knew he was totally different from our other strikers. We wanted to improve our team, particularly for the Champions League. We were very close to signing him, I know what the reason was [why he opted for United] but I won't say. It was not about money."
When Van Persie, 29, joined United in the close season he said he had "listened to the little boy inside me".
"In these situations, when you have to make a hard decision in your life, I always listen to that little boy inside me. What does he want? That boy was screaming for Manchester United," he said.
With Van Persie forming a deadly partnership with Wayne Rooney, United have scored 50 goals in their first 20 games - 12 more than City, who are the league's top scorers last season having racked up 56 goals in their first 20 games.
Sergio Aguero has been in superb form for most of the season but Carlos Tevez and Mario Balotelli have been off-beam and Edin Dzeko has been forced to operated much of the time from the bench.
"I am happy with my strikers because last season they scored more than anyone else in the Premier League," Mancini said.
"But when you can improve your team with other top players it is important to do it. With Van Persie you can sometimes play three strikers."
City, who won 4-3 at Norwich on Saturday despite having Samir Nasri sent off, host Stoke City on Tuesday while United make the short trip to Wigan Athletic where they lost last April - their only defeat in 16 meetings.
