"It's a big factor," Carragher told liverpoolfc.tv.
"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."