In a see-sawing game, Reds captain Virgil van Dijk headed the winner on 92 minutes to earn the 3-2 triumph.
Slot said afterwards: "It’s the second year in a row I had to celebrate my birthday on a Champions League night – and the second time in a row the players gave me a nice present because we won them both. I would like to ask UEFA if next year I can celebrate my birthday with my friends and family!
"Another great night here at Anfield. I think this is what the format is about, what UEFA probably wanted; to have already a first game in the group stage that could have been a quarter-final, semi-final (or) last-16 game.
"That’s also what you saw today – us playing really well, getting a lot of chances to finish the game off earlier and then you face a mentality team like Atletico. They always find a way to come back into the game and that’s what they did. The good thing for us is we have the same mentality."
On another late winner produced by his team, Slot also said: "Maybe at this moment in time the last part, although I think again it was a great game to watch not only for us as Liverpool fans, but for all the fans all around the world who love to watch football. I think that’s also part of our jobs, that people like what they see. That’s what we’re trying every time, but a game like this should not have gone to a late winner.
"Although, again, it’s not easy to beat Atletico Madrid because of their mentality, but I can come up with numerous moments where we could have scored the third one, which we didn’t. That’s maybe a bit different to the Burnley, Arsenal or Newcastle games where we didn’t create as many (chances) as we did tonight."
Isak debut
Slot handed a full debut to Alexander Isak and is confident the Swede will be stronger for the run.
He said, "I was positively surprised by how fit he was during that 60 minutes but that maybe, probably, tells you that it might be a difference to sign a 20-year-old from a different league or a 25- or 26-year-old that is used to playing in this league. Although he only trained for two weeks, he has so many games under his belt that he is probably more able to be ready for 60.
"But I was positively surprised how fit he was, I wasn’t surprised by his quality because that’s what we all know. You don’t have to be a manager to recognise how much quality he has. But it’s always nice to see if a player starts the way he starts, like Hugo Ekitike (who) started the same as he did. Yeah, a good start, only 60 minutes and now we have to build him up from here. But I can tell you he is not going to play 90 again on Saturday."