Owen spent most his three years with United as a bit-part player and he made just four appearances during an injury-ravaged final season with Sir Alex Ferguson's side.
The former Liverpool, Real Madrid, Newcastle and England star was released by United when his contract expired in June and Owen concedes it might have been better if he had asked for a transfer a year earlier.
After joining Stoke last week on a free transfer, Owen is in line to make his debut against Premier League champions Manchester City on Saturday and the 32-year-old is relishing the prospect of being involved in big matches again.
"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 said.
"In hindsight, probably with that extra year, it might have been better if I had moved in many ways."
Owen waited until after the season had started before agreeing to join Stoke on a one-year deal, but he insists he was always keen on Tony Pulis's side despite reports of interest from Liverpool, Everton and Sunderland.
"I spoke to the manager here a few months ago, so I knew there was a strong possibility that I would come here and I'll blame him for not making it happen sooner!" Owen said.
"I'm not sure why, but it just dragged on. I was eager to sign straight away.
"There were a couple of Premier League teams that showed interest, but this is a team on the up, I know the manager and a few of the players and it meant I didn't have to move my family as well.
"There were loads of things that ticked the boxes and I'm sure I've made the right decision.
"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."