The £35m signing rose highest to meet a Craig Bellamy cross three minutes from time to send the Reds in May's final against either Chelsea or Tottenham Hotspur.
"It's the best feeling ever. We worked hard and getting a goal at the end was great," he told ESPN. "I had a few chances and I probably should have scored earlier but I kept going.
"I've had some criticism but I have kept going. I believe in myself every day."
Carroll joined the Reds in January 2011 from Newcastle United.