Pulis' time as Potters boss came to an end on Tuesday, with a statement on the Staffordshire outfit's official website confirming they and the 55-year-old had mutually agreed to part company.
A message from Pulis to the club's supporters has now been published by The Sentinel, in which he said: "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."
Pulis said on Wednesday that chairman Peter Coates had been "truly a fantastic man to work with" and in the Sentinel piece, the former Portsmouth, Bristol City, Gillingham and Bournemouth boss again indicated that there is no animosity between the pair.
"I came back to the club in 2006 because of the Coates family, and Peter in particular, and that is a decision I have never had cause to regret," Pulis said.
"Despite the events of the last couple of days, my relationship with him remains, and I feel privileged to say that I can always call him a friend.
"It took a lot of faith and courage for him to return as chairman in 2006 - and then to bring me back as manager.
"I hope I have rewarded that faith and courage."
Pulis' second stint at the helm saw Stoke gain promotion to the Barclays Premier League in 2008 and achieve respectable mid-table finishes in the division in each season thereafter.
They were also losing FA Cup finalists in 2011 to Manchester City, with their appearance in the Wembley showdown earning them qualification for the Europa League, in which they reached the last 32 stage the following campaign.
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