The £35million striker was the Wembley hero for Kenny Dalglish's side, netting to earn a 2-1 win over Everton.
It was a rare moment of joy for the former Newcastle man, who has faced frequent criticism this season.
He headed in a free-kick from substitute Craig Bellamy in the 87th minute after Luis Suarez had earlier wiped out Nikica Jelavic's opener.
Carroll told ESPN: "It's the best feeling ever. We worked hard and getting the goal right there at the end was great.
"I had a few chances and should have probably scored earlier.
"But I kept at it and it was a great ball in by Craig, and I just had to score with that one and I did.
"It's a great feeling. I've had some criticism but I've just kept on going. I get the winner here and it's a great feeling.
"I believe in myself every day."
While Carroll was right in pointing out he should have netted earlier, most obviously when he missed an easier headed chance than the one he converted, Liverpool captain Steven Gerrard commended his spirit.
"He doesn't hide and he takes criticism on the chin," Gerrard said.
"That's what we bought him for, to score big goals, and he's delivered today [Saturday]."
Gerrard added: "We were superb in the second half. We showed superb character.
"Certain players have had criticism this week but they've stood up today.
"It's superb to be in the final.
"It's great to deliver and one more step and we're there."
Asked for his emotions at the final whistle, Reds defender Jamie Carragher told ESPN: "Relief really. Liverpool losing to Everton in the semi-final - it would have been a nightmare."
Carragher was particularly pleased with the outcome after being involved in the defensive mix-up with Daniel Agger that led to the Toffees' opener.
"Just relief that the lads went up the other end and showed what Liverpool is all about," he said.
"Everyone wanted Everton to win. (Everton manager) David Moyes said the whole country was with them. Well, we showed we're a special club, special fans. Not many teams can come back. We've done it again. We've got that ability to come back."
Carragher and goalkeeper Brad Jones were both quick to praise the strike force, particularly Carroll after his second crucial late winning goal this week.
"He'll be remembered forever for that," the former England international added.
"And Suarez I wouldn't swap for any other player in the league."
Australian goalkeeper Jones said of Carroll: "The media knock him but he's a fantastic guy. He works hard, does extra training and deserved this goal at Wembley.
"We knew they've got a lot of quality players and we had to deal with it and I think the boys at the back dealt with it well. I didn't really have a lot to do.
"At half-time we knew we had to step up a gear. We were confident but knew we had to put the work in."