Kitson moved to Fratton Park as part of the deal that took Marc Wilson to the Potteries.
Stoke's one-time record £5.5 million signing, who endured a well-publicised fall out with manager Tony Pulis, insisted: "I parted on good terms.
"Sometimes things don't work out for players and there are three or four of those at every club. It's difficult to put your finger on why that is.
"I haven't got a problem with anybody at Stoke. I have some good friends up there and it was a privilege to play with some great players like Tuncay and Glenn Whelan."