The Guinea international, a £50m signing from RB Leipzig, enjoyed a fine first competitive outing at Anfield in Sunday's 4-0 win over West Ham United.
Keita contributed to Liverpool's first goal of the one-sided match and was heavily involved throughout his 90 minutes on the field, more than living up to the hype that has surrounded his big-money move.
Milner, who started alongside Keita and Georginio Wijnaldum in a three-man midfield, says that the extra competition for a place in the side is only a good thing.
"Naby Keita is a good player, you can see that and he's only going to get better," he told Sky Sports News. "Coming into a new team is not always easy. You can only imagine how good he's going to be with more time with the boys.
"He's top quality and like all the signings we've brought in there's even more competition. That's what you want.
"There is expectation at the beginning of the season and everyone wants a good start. We've made some new signings and it was going to be a tough start.
"Last year was a long season and with the World Cup boys coming back in with such a short rest, they have done well. I've done it before and know how hard it is. It's the same with all teams with international players out and the first game after pre-season is always tough."