Owen was released after having made only four first-team appearances for United last season.
The 32-year-old was urged to remain at United by manager Sir Alex Ferguson a year ago.
Owen has now joined Stoke City on a one-year contract.
"In hindsight, probably with that extra year, it might have been better if I had moved in many ways," he said.
"I was on the bench a lot of the time, but then when the manager says 'you have a big role to play and we want you to stay for another year', it was great to hear that from someone like Sir Alex Ferguson."
He added: "I want to perform and I want to finish my career on a real high. I'm still only 32 and I still feel as if I have a lot left in me.
"I've always scored goals, no matter what team I have been in, so as long as I can stay fit and healthy, then I'm sure I can do that here at Stoke."