The Reds won 6-0, with Alexis Mac Allister scoring twice and Mohamed Salah on the scoresheet for the first time since November.
The result sees Liverpool automatically reach the the round of 16.
Slot said afterwards: "It's what you want if you start the Champions League season – you want to finish top eight. That helps, of course, because you skip a round and sometimes you can have a really hard team to play against in a round like that, which is shown by the teams you just mentioned.
"So, we are happy that we are going straight away to the last 16, especially because it's only two years ago that we were playing Europa League and we went out in the quarter-finals against Atalanta."
The Dutchman also said of the result: "We have all the respect for the team we faced tonight, I expect Newcastle to be a stronger side than Qarabag – although Qarabag showed this season that they've been a very good team. But still, we hardly conceded anything.
"There weren't six, seven or eight minutes where the other team was better than us, and that's the maximum usually in our games – the other team is better than us and then we always concede. But today we made sure there were no minutes that the other team were better than us and that always helps.
"I think set-pieces played a vital role in our Champions League campaign until now and tonight again, because the 1-0 was a set-piece and the 3-0 was a set-piece. That gives a complete different look and feel to a game.
"All of a sudden, you're 3-0 up and then people are usually much more positive than a 1-0 lead. Very positive about our game, very clinical in both boxes – although after the 2-0 I think we had multiple chances to make it three."