United are five points clear at the top of the table.
Meulensteen said: “Robin gives the team an invincible feeling.
“All the players have that same buzz. They think ‘we’ve got Van Persie. With him we are always going to score. We can always give him the ball and he will always do something magical with it.’
“In the last few seasons, we had squeezed everything out of our star players and last season we were just not good enough.
“As a club we had to make sure that we would not underperform again. With Robin we have a world-class player in our ranks again. He’s a really world-class act. As one of the biggest clubs in the world we really needed a player like him.”
Meulensteen believes that the rest of United’s squad recognised a kindred spirit in Van Persie when he announced his intention to move to Old Trafford to win trophies.
United’s gain has been City’s loss. The Dutchman said: “With his personality, it was easy to get a warm welcome from the rest of the squad from the first moment.
“Robin is not the kind of player who says, ‘Here I am’. Robin is an absolute professional. He’s a fantastic trainer and he delivers on the pitch.
“That creates a security for players. They feel nothing bad can happen to them because we have got Robin van Persie. We really missed that kind of influence last season.”