The Reds got their 2018-19 campaign off to an ideal start as goals from Mohamed Salah, Sadio Mane (2) and Daniel Sturridge saw them run out convincing winners at Anfield, leaving them top of the table after the first matchday.
The performance suggested that predictions Liverpool will be Manchester City's closest challengers this season could prove accurate, but Milner insists that his side are solely focused on continuing their encouraging start to the season.
"That's for other people to talk about. You guys (media) are going to discuss it, we just want to start the season well and keep improving as a squad and see where that takes us. Obviously it is early days and the first game of the season you want to get off to a good start, it is very important," he told reporters.
"It is never easy coming out of pre-season when you have players returning at different times due to the World Cup but you just want to get off to a good start and get a win. I thought it was a good performance and I am sure it will improve as the season goes on. It was a good starting point, plenty we can work on but the best possible start and hopefully we can kick on from there.
"We feel we can beat anyone on our day, we have proved that but it is about having that consistency and we will know how difficult it is to win a league title and have that consistency and do it over 38 games. For us, we will just let other people talk about the challenges, it is down to us to go out there and perform and get as many points as we can."
Liverpool are back in action on Monday night, when they face Crystal Palace at Selhurst Park.