Carew scored three goals in Villa’s 4-2 win over Reading in the quarter-final on Sunday.
Reading had a 2-0 lead after the first half.
“We had a very hard and difficult first half but we managed to come out after the break and lift our game,” said Carew.
“We had to look at each other in the eyes at half-time and knew we just had to 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 didn’t seem to be up for the fight.
“But, in the second half we went out there with more desire, and showed that we really do want to go further in this competition.”
Carew is keen on a return to Wembley, following their Carling Cup final defeat to Manchester United.
“We’re really pleased to have a chance to get to another final. We managed to do it in the Carling Cup and now we’ve got a chance to do the same in another cup,” said the Norwegian.
“We will do everything we can to get there.
“We want to make amends for losing the final and I think we can turn last week into a positive.
“The FA Cup is an even bigger cup, and even more important, so it will be even greater to go all the way in that competition.
“The players will have learned a lot from last weekend. It was a great experience, the big scene of Wembley, and everything.
“It makes you want more of the same sort of occasion. Everyone dreams of getting to the final again and we’ve got another chance.”