The striker joined The Potters on a three-year deal on Friday for a club record fee of £5.5million.
He admits he would have liked to stay at the Madejski Stadium if Reading had managed to avoid relegation from the top flight last season.
Elaborating on why Stoke was such an attractive proposition, Kitson stated that it would have been wrong to accept an offer from a Premier League club if he did not feel he was going to play regularly.
"Reading are a club that I would have hoped to finish my career with," Kitson told Sky Sports News.
"I just wanted them to be in the Premier League so badly and I was distraught when we go relegated.
"I think, if you say you want to play Premier League football, and then go to a team and sit on their bench, I think that is hugely disrespectful."
Kitson also paid tribute to new boss Tony Pulis, adding: "The manager's enthusiasm is almost overwhelming.
"He's so keen to do well. He's talking about bringing in new players and taking the club forward
"You look at the teams you have to compete against and the gulf is that much wider than it was last year, and as a newly promoted team you are almost a target to be put in your place."
Pulis, meanwhile, is confident that the 28-year-old will make a huge impact at the Britannia Stadium.
"His goalscoring record is very good in any league he has been in. He has scored goals in the Premier League and he has got something to prove as well, with Reading having been relegated," said Pulis.
"He's got that little bit between his teeth that he wants to prove he is a Premier League player."
SkySports