Kitson signed a three-year deal with the newly-promoted side on Friday but it has since emerged that there was late interest from two other top-flight clubs to secure the services of the 28-year-old.
Fulham and Wigan were linked with bids earlier this summer, and a reportedly last-gasp bid from West Brom.
"I had the chance to go and earn a good living elsewhere, but it would be disrespectful to a club like Reading to leave them to go and sit on the bench somewhere else," he told the club's official website.
"I want to play 38 games and I can do that here at Stoke."
The Potters have been backed in some quarters for an instant return to the Championship next season but Kitson believes his new side can follow the example of his old one Reading and defy their critics.
"It's hard, it's difficult," he said, "but as a newly-promoted team what you do have in your locker is the fact you're an unknown quantity and you have to utilise that and play to your strengths.
"We can't get near Man United in terms of spending, but how much do they know about us?
"You can roll over and die, or you can compete, and if I didn't think we could compete I wouldn't be here.
"The manager's enthusiasm is infectious. He wants to do well and wants to bring in more faces."