Pulis, 55, left the club by mutual consent on Tuesday and has now sent a message to the Potters' supporters via The Sentinel.
"It is all over for me now and, believe you me, I wish the club all the best in the future," Pulis said.
"Of course I am disappointed I cannot carry on in a job I have loved from first minute to last. But I accept the club's decision to move things in a different direction because that is the right of any owner.
"The journey stops here, but what a journey. And you, Stoke City's wonderful support, have played such a massive part in the distance we have travelled over the last 10 years.
"That is how vital your support is. And that is why I urge you (for one last time) to get behind the new manager just like you got behind the old one."
Mark Hughes, Roberto Di Matteo and Gus Poyet are among the leading candidates to take over the reins from Pulis.