Recently bemoaning the reduced output of City forwards Tevez, Sergio Aguero, Edin Dzeko and Mario Balotelli this season, City's Italian manager also claimed that Van Persie had "made the difference" for United and "changed the situation" between the two clubs.
But former United striker Tevez, who has scored nine goals in all competitions for City this season, insists that Mancini's praise of Van Persie will inspire the club's front players to redouble their efforts as they attempt to overhaul their neighbours.
"Those words were a motivation for the strikers," Tevez said. "We know that we need to carry on fighting. It also happened last season that United lost some games and we were back on track, so we will keep doing our job.
"We can do it. There's a long way to go and a lot of games to play. We want to keep winning, to keep fighting for the title and I will try to help us to compete on both fronts, in the Premier League and FA Cup, and try to win both."
City, who travel to Arsenal on Sunday, overturned an eight-point deficit in the final six games of last season to deny United the title and Tevez believes that the memory of their collapse will ensure that United continue to look over their shoulders at Mancini's team.
"That's the emotion of the Premier League," Tevez said. "It's always a fight to the end, and if United lose one game, we'll be back on track and getting close to them. They will know that."
In the absence of leading scorer Aguero with a hamstring injury, controversial forward Balotelli is expected to be named in the squad to face Arsenal after playing for City's under-21 team on Monday to boost his fitness.
City are prepared to sell the Italian forward this month, but comments from AC Milan owner Silvio Berlusconi describing him as a "rotten apple" appear to have ended the prospect of a move to the San Siro.
Napoli are keen to sign Balotelli and although financing a deal for the £20million-rated forward, who earns £170,000-a-week at the Etihad Stadium, would be difficult for the club, manager Walter Mazzarri believes he could tame the volatile 22-year-old.
"I do not know him personally." Mazzarri said. "I spoke to him once a few years ago at a hotel in Sorrento and he made a good impression on me. But only those who know him well can say what kind of problems he might create in training.
"I've got a bit of experience, though, and it would be stimulating to work with a talent like his, but I don't know if that would ever happen."
Aurelio De Laurentiis, the Serie A club's president, also opened the door for business with Balotelli, though not as part of a potential swap deal for Napoli striker Edinson Cavani. "Are City considering letting Balotelli go so they can make a move for Cavani? I would prefer to see Balotelli playing with Cavani here at Napoli but we must be cautious," he said.
City, meanwhile, have been told by Northumbria Police that no action will be taken against defender Aleksandar Kolarov following allegations of a clash with supporters during the 3-1 victory at Newcastle United last month.
The Serbia international was reported to have been involved in a confrontation with supporters brandishing an Albanian flag at St James' Park, but following an investigation, Kolarov has been told that he has no case to answer.