The Austrian joined West Ham earlier this week in a £25m move, claiming that the 'Hammers' were a 'bigger and more ambitious club' than his former employers.
In an interview with 'talkSPORT' Coates revealed his frustration with the manner of the player's exit.
"I was very disappointed because he is a wonderful player," explained the Stoke chairman. "We are disappointed in him personally and [with] the people around him."
"We resurrected his career. Our manager and coaches worked very hard to improve him - and they've done that. They made him a name in the game."
"Last year we put so much effort into giving him a long-term contract which was supposed to be it, and first thing we get in the summer he comes back and wants to leave."
"So yes, we are very disappointed but the team is more important than the individual," Coates concluded.