The Reds took a step closer to winning their first piece of silverware since 2006 when they dispatched Chelsea 2-0 at Stamford Bridge on Tuesday to reach the semi-finals.
Carragher, who was making his first appearance in over a month after recovering from a calf injury, insists it is a competition Liverpool are eager to win.
"I've played at Wembley once or twice for England but I've never done it for Liverpool. I'd love to do that," he said.
"When we have reached cup finals in the past they have been in Cardiff, so I've never been there with Liverpool.
"There is still a semi-final to play over two legs and there are some massive sides in there so it is going to be very tough. We'll take the semi-final very seriously."
Craig Bellamy inspired the win in west London by setting up goals for Maxi Rodriguez and Martin Kelly.
England Under-21 right-back Kelly nodded home his first goal for the club, topping a strong performance that Carragher believes is just the start of things to come.
"Kelly is a young lad coming through, he's still learning the game. He can learn off Glen Johnson, England's right-back," he said.
"But hopefully in the future Martin Kelly will be in that position himself and he showed that against Chelsea."
It had taken academy product Kelly 35 appearances to finally open his Liverpool account and the 21-year-old has now set his own sights on reaching Wembley.
"I'm made up with the goal and we're all happy with the team performance," he said.
"It was a great cross from Craig and I managed to get a free header. You've got to take them. It's been a long time coming.
"We were attacking the end with all the away supporters and it was brilliant seeing all their emotions as they celebrated. It's fantastic to get a goal for such a big club.
"We've gone to Chelsea twice now and got two victories and we're all over the moon with that.
"We're looking forward to the semi-finals and hopefully getting to the final at Wembley.
"If you ask any young lad, they dream of one day playing at Wembley and I'm the same.
"I can't wait for the next round and hopefully I'll be a part of that."