The England international was being celebrated around the world after his goalscoring performance in victory at Leicester City.
"He will only get better," Milner says. “If he continues to do what he is doing in the near future, given that he is still young, people will talk about him for a long time. His mentality is one of the things that impresses me the most.
"You can admire his technical qualities, but his mentality is great. His whole life is great.
“I think we will see much more of Trent, he will get better and better and that he will be a great footballer for Liverpool for many years to come. The road is long and we don't want him to become arrogant or conceited, but that won't happen."