The Reds stumbled to a 2-0 defeat against Zenit St Petersburg in the first leg of the round-of-32 match in Russia yesterday.
"We've got a mountain to climb but the club have climbed those type of mountains in the past," the Liverpool Echo quotes Carragher as saying. "It's something we have to look to do again at Anfield next Thursday.
"It's a disappointing night for us but we have to dust ourselves down and try to come back from this. If we achieve that it will be a great night.
"Of course they are big favourites now but it's not over. It will make for a great atmosphere at Anfield and if we can get that first goal then the place will be bouncing."
Meanwhile, the Reds are unlikely to qualify for the Champions League next season as they currently sit ninth in the Premier League table.