Despite falling 1-0 down to a Jelavic goal, Luis Suarez and Andy Carroll capitalised on slack defending to take Kenny Dalglish's side to another Wembley final
Jamie Carragher spoke of his relief after making a mess of a clearance in the first-half and gifting Nikica Jelavic with the chance to open the scoring.
“I'm relieved,” he told ESPN. “As a local player losing to Everton would have been an absolute nightmare.
“I was involved in their goal at the start and if we'd lost that 1-0 I don't think I'd have ever recovered to be honest!
“It was one of those things that happens but I'm just relieved the lads went up the other end and showed what Liverpool are about.
“Everybody wanted Everton to win, David Moyes said the whole country is with them.
“But Liverpool is a special club with special fans, not many teams would come back from there. We did it before in 1986 when Everton were 1-0 up at half-time.
“We've done it again – showing that ability to come back.”
Steven Gerrard skippered the side to victory and spoke of the tough game the Toffees gave the Anfield club.
“It was very tough, Everton played very well – they're a good side, with a good manager," he explained.
“We expected a really tough game but we were superb second-half.
“We showed great character. Certain players have had a lot of criticism this week but they stood up today, they were counted and superb for us.
“It's superb to be in the final and we do it for these people. It's just great, one more step and we're there.”
Third-choice keeper Brad Jones stepped in for the suspended Pepe Reina and Doni and performed well between the sticks.
He added: “We knew that the game was going to be fairly even and that they have a lot of quality players – a good front-line.
“So we just had to deal with it. The boys at the back are fantastic players and dealt with it well – I didn't have a lot to do."
A half-time turnaround gave Liverpool the impetus to go and claim victory and Jones said: “We knew we had to pick it up.
“At half-time we all spoke and knew we had to step up a gear. We knew we had a half left to play and we were confident.”
Although he played his part in the run to the final, Jones did admit he knew he would be taking a back-seat for the final.
He concluded: “In the end, Pepe is the main man.
“We don't dispute that, he's been top drawer for the last five or six years so I'm hoping he'll be proud of it.
“I'm hoping he'll have the chance to come back here and hopefully pick up the trophy.”