Alisson arrived at Anfield for £65 million ($83m/€71m) from Roma last month – a move that established him briefly as the most expensive keeper of all time before Kepa Arrizabalaga joined Chelsea from Athletic Bilbao.
"He's been brilliant since he came in," Robertson told Liverpool's official website, with Alisson's footwork – most notably an impudent dink over Brighton forward Anthony Knockaert – having also caught the eye.
"He's a real presence at the back, you can see him coming out for corners and crosses and you've seen his wee chip got applause from the crowd, but I'm not sure if the gaffer wants to see that too many times.
"But fair play to him and that's the confidence he's playing with and it breeds onto the defence. When we needed him he came alive and palmed it away. Fair play to him so far, he'll be delighted with three clean sheets and long may it continue."
Robertson's fellow full-back Trent Alexander-Arnold added his voice to the plaudits.
"I think he's a world-class goalkeeper and he's shown it," the England international told his club's website.
"With his composure on the ball he is probably one of the best in the world and he definitely showed it that with the chip - hopefully he doesn't have to do that again."