Liverpool were beaten 2-0 at Valencia's Mestalla Stadium, for which they were slaughtered in the media.
But Carragher thinks that Liverpool must compete on a level they never got close to achieving in Spain.
He said: "We let ourselves down over there. We never even put up a fight or a battle in Valencia, especially in the first half. I don't know why.
"We were made to be the worst team in the world afterwards and that was over the top. But we know we have to do much, much better."