The Reds overcame their Merseyside rivals 2-1 at Wembley to book a final with Chelsea.
David Moyes's men had gone into the break leading 1-0 and Carragher said that he would have been devastated had the Toffees gone on to win.
"I was close to tears to be honest. I think if we'd lost that game I don't know if I'd have ever recovered," admitted the 34-year-old.
"As an Everton fan as a kid, this was the biggest derby I've ever played so I'm delighted the lads have done it and helped me out. It's one of the biggest games I've played in, right up there with the Champions League final. The thought of the stick me and Stevie Gerrard would have got on the streets of Liverpool if we'd lost that game.
"We've played in big finals in Champions League and FA Cup but this was right up there because of who we were playing. Because it was at Wembley it felt more like a final."
Liverpool staged a miraculous comeback in the 2005 Champions League final over AC Milan, having been 3-0 down at half time.