Van Persie has revealed on his official website he will not extend his contract, which runs out at the end of the 2012-13 season.
Smith does not believe, however, that the Dutchman was swayed to turn his back on the club by the riches the likes of Manchester City can offer.
"From what I have heard from people close to Robin he's not motivated by money," he said.
"I think at his age, he's 28, it's about winning medals. He's in his peak years now. I truly believe in this case he wants to win things in the next few years when he can.
"But Robin van Persie is looking at the next few years when he's 28, 29, 30; he thinks they can't win trophies. You don't want to say it but you probably have to agree with him."