Coutinho struck from 30 yards with just four minutes remaining as the Reds snatched a 1-0 victory from an otherwise drab contest at the Britannia Stadium.
Milner told LFC TV: "I obviously saw him do it a few times last year so to do it when he is on my team is nicer.
"That is what the game needed. It was a tough game, it was a battle. I thought we defended really well and it was going to take a moment of brilliance to win the game and we managed to get that."
