Villa had to come back from 2-0 down at halftime to beat the Royals 4-2 - thanks mainly to Carew's hat-trick.
He told Villa's website: "We had to look each other in the eyes at half-time and just go out in the second half and do better than we did in the first.
"We just seemed a bit surprised by everything - the conditions were a bit difficult and the ball was in the air a lot. We just didn't seem to be up for the fight. In the second half we went out there with more desire and really showed that we do want to go further in this competition.
"The way we came back to score four goals was one of the performances of the season. We showed we have our head in the right place again. I think we can turn last week into a positive and I think we have done.
"This is an even bigger cup and even more important so it will be even greater to go all the way here.
"We are just doing everything we can for the fans, for the club, for ourselves to have that beautiful experience again. The players will have learnt a lot from last weekend. It was a great experience, the big scene of Wembley and everything.
"Everyone dreams of getting to the final again."