It was the type of performance which suggested a threat to Manchester City’s title defence but Milner, said: “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.
“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.”
Milner, at Celtic Park to publicise a charity match next month where he will organise a team to take on former Hoops midfielder Stiliyan Petrov’s side, added: “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.”