Karius left the Reds for a two-season loan with Besiktas.
Gillespie told LFCTV: “I think it's a massive decision for him but I think it's the right decision as well.
“He's still a young man and there's loads of potential for him to become a top goalkeeper, and I am sure he will some day. I think it's the right decision.
“Hopefully he goes there and is a success. Who knows what can happen. We've seen players go and then come back and be superstars.
“He's gone to a top club in Turkish football so there will be big games there and he will have to perform."