Carew was on the mark in their FA Cup victory over Brighton.
"Everything is going fantastically for me personally and for the football club," Carew told Stoke's official website.
"To go out there and do such a professional job was hugely satisfying.
"I feel at home here, the supporters have been fantastic with me and all of the players, management and everyone else at the club have made me feel unbelievably welcome.
"I was obviously very happy to get a goal, but for me it is about looking forward now and I just want to make sure that I keep doing well for the club and keep doing what the manager and the supporters expect of me."