Milner, 32, dispatched his 50th Premier League goal just beyond the hour before Alexandre Lacazette's fine finish eight minutes from time earned the hosts a point.
Virgil van Dijk went close on two occasions and Sadio Mane had a goal controversially ruled out for offside all prior to the opener.
"[We are] very disappointed really, which is a good thing I suppose, playing away at Arsenal," Milner told his club website.
"To be 1-0 up in the second half and not see it out, we are disappointed.
"With the chances we created we should have scored a few more goals.
"It's pleasing we are creating those chances, but we could have been a bit more ruthless and maybe not put as much pressure on ourselves not to concede to win the game."
The Reds have now been held to draws in two of their past four Premier League fixtures, having been fortunate to escape with a stalemate against City last month.