After 26 years at Old Trafford, Sir Alex Ferguson has called time on his career at United and will be succeeded by Everton manager David Moyes this summer.
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"Everybody wants to work for each other and share the success," Van Persie told MUTV.
"I'm 100 per cent sure we will play for trophies every year and, hopefully, win a few every year. That's our standard for this team.
"This is a great team and, hopefully, we can go for even more trophies. I'm sure we can. Of course, we get a new manager next year and everybody is looking forward to that.
"It's a new challenge for everyone. We'll have a nice break now and then we go again."
Van Persie also paid tribute to Paul Scholes, who retired at the end of the season, and the 29-year-old striker maintains the midfielder, along with Ryan Giggs, have become role models at the club.
"I would love to emulate them," Van Persie said. "I would love to play on as long as possible.
"Watching Scholesy and Giggsy and the way they look after their bodies - they are true examples for young and old, and that's what I want as well."