"I have a feeling we can do much more and that we can win many more trophies. I've had a year to work with everyone and now the whole [coaching] staff is changing which makes it a new challenge," Van Persie told the Dutch football union website on Wednesday.
"I've got to know the players through and through and I've a feeling they have a lot more [success] in them. A whole lot more," he added.
"The season began as a nice challenge but you never know how these things will turn out. But now I have a sense of pride, it was a great season. A pressured year."
Van Persie, who helped United win the Premier League title last season after joining from Arsenal, said he would have liked to have worked longer under Ferguson who retired last month after 26 years at United and was replaced by David Moyes.
"I'd have preferred it if he'd stayed a few more years but I understand his decision. I'm even prouder that I could work under him for a year. I could see he was a legendary man."
Van Persie said title success had brought great satisfaction and happiness but he was more pleased with the way it was achieved.
"If you saw how we worked every day. How we studied the opponents and the way they played," he said.
"How we prepared. Every day we did extra work and watched videos. Every small step eventually delivered the championship. I think that the route to the title was nicer than the winning itself."
Van Persie is expected to win his 75th cap on Friday when the Dutch play Indonesia in a friendly in Jakarta. They have another international in China next week.
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