Mancini expressed his unhappiness at losing out in the battle to sign Van Persie, but Tevez insists the current squad can prove they are just as prolific in front of goal.
"Those words were a motivation for the strikers," the Argentinian told several newspapers. "We know that we need to carry on fighting. United lost some games last season and we were back on track, so we will keep doing our job.
"There's a long way to go and a lot of games to play. The emotion of the Premier League means it's always a fight to the end.
"If United lose one game, we'll be getting close to them. They will know that.
"We want to keep winning, to keep fighting for the title. I will try to help us to compete on both fronts, the Premier League and FA Cup, and try to win both."