Van Persie was asked if rival clubs would sense weakness in the wake of Sir Alex Ferguson's retirement.
Van Persie said: "Yeah, of course they will but they can think what they want to think. It doesn't matter to us. What matters to us is the way that we work. Trust me, we will work very hard. It's a huge challenge to all of us and it's one we are looking forward to."
Van Persie transpired to be Ferguson's last major signing when he left Arsenal to join United for £24million last August. He has proved a huge success at Old Trafford, scoring 30 goals in United's march to the title, but is confident he can do even better this season.
"Of course it was a great year last time," he said. "It was my first year with him (Ferguson) and the first year at the club I had with him.
"But now it's a new year and I am very much looking forward to it with a new manager and great new staff. For now we have the same players."