Jurgen Klopp’s side put down an opening-day marker in the Premier League with a 4-0 home victory over West Ham United.
Many are tipping the Reds to push reigning champions City all the way this season, as they look to end a 28-year wait for a league title.
But Milner has urged his side to show their best form on a more consistent basis this season and block out title talk from elsewhere.
"That is for other people to talk about really,” Liverpool’s vice-captain said. "Obviously, you guys are going to discuss it.
"For us, we just want to start the season well and keep improving as a squad, and see where that takes us.
"We feel we can beat anyone on our day and we have proved that, but it is about having that consistency.
"We all know how difficult it is to win a League title, to have the consistency over 38 games.
"We will let other people talk about the challenges, and it is down to us to just go out there and perform, and get as many points as we can."
Much has been made of Liverpool’s summer transfer business, with Klopp’s side spending more than any other Premier League team ahead of the new season.
Fabinho, Xherdan Shaqiri and Alisson Becker have all arrived at the club, with Naby Keita also joining up after the Reds agreed a deal to sign him from RB Leipzig last summer.
Milner has praised the club’s recruitment and says the Reds’ latest additions have had no trouble settling in.
"You look at the team that started the game (against West Ham) and the players on the bench - and even the players who were injured and didn't make the squad,” he said.
"It is very strong and that is exactly what you need, all the best teams have that strength in depth and competition for places.
"It is not easy changing teams and learning a new system as well - and the way we play is different to a lot of teams, so it is going to take time.
"But they have settled in well already and I am sure they will get better and better."