Van Persie won his first league title as a professional in what turned out to be his only season under Ferguson at Old Trafford following a £24m move from Arsenal.
"I want more now," van Persie said. "I want more medals now because I now know how it feels. It gives you the taste for more. Hopefully next year we can win the double, or even more.
"It will be a new era and I am looking forward to it. It is part of our job. We have to deal with a new situation. That is how it is.
"First we can enjoy what we have achieved this year. Then you start to think about next season and, of course, we are looking forward to it.
"We have a new manager - maybe new players coming in. Wilfried Zaha is coming from Crystal Palace and there may be more, there may be some leaving, no-one knows.
"It is a challenge and everybody knows what our standard is. We want to win the league again and then, hopefully, add one or two trophies to that."