"It's a big factor," Carragher told liverpoolfc.tv.
"It's one of the main reasons why we've done so well in the Champions League. Obviously the players and the manager have played their part, but I'm sure everyone would recognise that the supporters played a massive role in getting us to Istanbul and getting us to Athens, and we need them at the moment, because we haven't done as well as we would have liked in the first three games.
"The players and the manager need to play their part, but I'm sure the Kop and the supporters will also have a massive part to play tomorrow."
The Reds are currently bottom of Group A with just one point from three games played.
"That is going to be massive for us, it means that Anfield and our supporters can come into play to give us a lift to push us when we need it.
"It is three cup finals for us now and we know we can do it. But we have made it a lot tougher than it had to be.
"But I can assure everyone that we will be ready for Besiktas and this time we will take our chances."