Idris El Mizouni scored the only goal of the game three minutes into the second half, as the Potters suffered their third defeat in five Sky Bet Championship games so far this season.
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Potters sporting director Jon Walters told the club website: “My role as sporting director is to make tough decisions that serve the long-term interests of Stoke City.
“After ongoing discussions with John Coates, we feel the time is right for a change in direction to bring success to the club.
“We have a young, dynamic squad that is eager to develop and a clear vision of how to achieve success, and we hope to announce a new appointment shortly.
“We will need the fans, staff and players united in support to achieve our goals.
“As always in football, these decisions are difficult, and we wish Steven and his staff all the best for the future.”