The Reds won 3-1 at San Siro stadium through goals from Ibrahima Konate, captain Virgil van Dijk and Dominik Szoboszlai. Christian Pulisic had given Milan a third minute lead.
Asked if it was the perfect birthday present, Slot said: "Yeah. I said a few times already, normally you celebrate your birthday with your friends and your family. But this was a real good alternative to play a first Champions League game against a special club for Liverpool, but also a special club for Dutch people in a nice venue.
"Then to win it the way we did after going 1-0 down after five minutes with the result of Nottingham Forest still in our head. I think it was very good to see how they took the game in their hands the players and in the end we scored three goals and won 3-1."
On conceding early, Slot also said: "It sounds a bit weird if you play three, four, five minutes and we already conceded one chance, which was offside, and then afterwards you concede a goal, that I'm going to tell you now that we didn't even start bad. I think we took control of the game from the start. But in the first five minutes we also lost the ball from two choices that were not the best to make and then they could counter-attack us.
"Afterwards we dominated possession even more and that didn't lead to counter-attacks from them. Although it sounds weird to say that we started well if you concede two chances, but we took control of the ball from the start of the game. Except from the first five minutes where they had two counter-attacks, I think we dominated possession and created chances as well."