In miserable conditions at the Etihad, the former England man opened the scoring in the 51st minute from the penalty spot after Gael Clichy's foul on Roberto Firmino.
However, following chances at both ends, Sergio Aguero levelled the scores with 21 minutes to go and, despite the best efforts of both sides, they could not be separated.
The result leaves fourth-placed Liverpool a point and a place behind City, although the Citizens do have a game in hand.
Speaking afterwards, Milner admitted the open nature of the clash meant either side could have won but believes that in the end, the draw was a fair result.
Milner told Sky Sports: "Both teams went for it. I am sure it was good for the neutrals to watch. We are disappointed that when we have been up we have not got three points. A draw was fair in the end.
"They are such a good team. They've got runners everywhere, they're all sharp. It is not the easiest of days coming here. We can't be too disappointed with a point."