The Norwegian returned to the starting line-up for Villa's scoreless draw with league leaders Chelsea at the weekend.
Carew, who has worked with Houllier previously at Lyon, feels that Villa will continue to improve, as a result of the Frenchman's methods.
"Always with a new manager you have some new ideas and I think we've done quite well since he's come," said Carew.
"The team is very strong. It's important to develop with the games coming up.
"We work hard on new things and that's what we're all interested in. That's what we're here for - to make this club better and make the results better, to achieve goals and improve each season.
"If that means more work and harder work, which it probably does, then that's good."
Carew expressed his satisfaction with Villa's drawn result against Chelsea, despite being denied a golden opportunity by Petr Cech early on.
"We showed that we're really fit and we managed to keep them away and played out football quite good, especially in the first half," he added.
"So we have to be satisfied with a point against the champions of last year, take lots of positive things from the game and try to continue.
"We had chances but they had chances as well. In the first five minutes, I had a shot and as soon as I hit the ball I thought it was a goal but Cech managed to get his finger on it.
"They had a couple of chances too and they probably had the best one as well with Nicolas Anelka."