Andy Carroll headed home an 87th minute winner at Wembley.
Gerrard said: "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."
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.
"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."