“It's an unbelievable feeling to have that relationship with the fans," Robertson told the Liverpool Echo.
“To hear them singing your name, it gives you a wee bit of a lift. I'm grateful for how they have welcomed me.
“You want your fans to be on side. I feel like they have taken to me and I've taken to them quite quickly."
The Scot continued: “I might not have the best of games every now and again, but I always leave everything out there.
“Whether things are coming off and whether I'm finding people with my crosses, I always give 100% - that's the way I've been since I was a kid.
“It's no secret that my family and I used to go and watch Celtic at home. I've always had that passion for football in me. That's not changed from being at Queens Park, Dundee United, Hull or Liverpool. Wherever I've been, I've given my all.
“I think Liverpool fans maybe enjoy seeing that work rate. As a team we are all working incredibly hard and that's enabling us to produce performances the fans can enjoy."