The Norwegian striker joined the Potters until the end of the season last week and will hope he finds it as easy to score for Tony Pulis' team as he did against them, having netted three goals in four matches for Villa.
Carew told the Stoke Sentinel: "I had a fantastic relationship with Villa fans, but that's now over. Hopefully I can now come here, do well and have a great relationship with Stoke fans. I knew I had scored against Stoke before, but I didn't know it was that many."
The 31-year-old left Villa Park after reportedly falling out with manager Gerard Houllier, who also sold the striker at Lyon, and Carew declared himself inspired by his move to the Potteries.
"It's a long story with Houllier, but I had three fantastic years at Villa, scored lots of goals and proved a point there," he continued. "What inspires me is coming to a new club, meeting new players and playing in a new environment.
"I could have stopped playing now and I would have had a fantastic career and done everything I wanted to. But I don't want to stop. I am inspired by this move."