The former England forward, 32, signed a one-year deal at Stoke last week.
Owen was urged to stay at Old Trafford by Alex Ferguson a year ago but went on to make only four first-team appearances for United in 2011-12, the last of which came in November.
He said: "In hindsight, probably with that extra year, it might have been better if I had moved in many ways.
"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."
Owen could make his Stoke debut against Manchester City on Saturday - a team he scored a dramatic injury-time winner against for Manchester United in September 2009.
That was probably the highlight of the striker's injury-hit time at Manchester United and he is looking forward to making a bigger impact at Stoke.
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."