Sir Alex Ferguson's retirement after 26 years in charge has heralded the arrival of David Moyes, who despite more than a decade in charge at Everton did not win a trophy.
But Van Persie, last season's golden boot winner as United claimed their 20th league title, said a change at the top did not mean the players would view the situation differently.
"It will be a new era and I am looking forward to it," the Holland international told MUTV.
"It is part of our job as well. We have to deal with the new situation and how it is.
"It is going to be a new challenge, with a new manager, maybe some new players coming.
"[Wilfried] Zaha is coming in from Crystal Palace, maybe some more. Maybe some will leave, nobody knows.
"But it is going to be a new challenge and everybody knows what our standards are: we want to win the league again and then hopefully add one or two trophies to that."