The Manchester United striker has admitted he wishes he could have played under the Scottish coach for longer but is confident of success under new boss David Moyes
The Dutch striker proved to be Sir Alex's final marquee signing, arriving from Arsenal for around €28 million last summer and scored 26 league goals as United claimed their 20th championship.
Van Persie realises that there will be changes at the club following the Scottish coach's departure, but is relishing the challenge of ensuring continued success under new boss David Moyes.
"I have a feeling we can do much more and that we can win many more trophies," the 29-year-old told reporters.
"I've had a year to work with everyone and now the whole coaching staff is changing which makes it a new challenge.
"I've got to know the players through and through and I've a feeling they have a lot more in them. A whole lot more.
"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 was full of praise for his former manager and admitted that he only wished he had played under Sir Alex for a longer spell.
"I'd have preferred it if he'd stayed a few more years but I understand his decision," he conceded. "I'm even prouder that I could work under him for a year. I could see he was a legendary man.
"If you saw how we worked every day. How we studied the opponents and the way they played. 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."