Diogo Jota's strike on 57 minutes earned the Reds a 1-0 win at Anfield.
Slot said afterwards: "Hard-fought, definitely, but that was no surprise. Everton were nine games in a row unbeaten, hardly ever concede a goal, hardly ever concede a chance, defend with 10 players apart from Beto in and around their 18-yard box. With players like (James) Tarkowski and (Jarrad) Branthwaite it is almost of no use to bring a cross in because they head every ball away. So, they are a team that is difficult to play against because they are also a threat on the counter-attack with Beto.
"Every throw-in they get and every free-kick they get against us, you have to defend that and that's what makes it so difficult.
"What I liked much more today than I did at Goodison Park... at Goodison Park we had ball possession but we only had ball possession with our centre-backs and full-backs and today only the first half. I think if I say 10 or 15 times that Lucho Diaz was one-v-one against Jake O'Brien, I don't even think I exaggerate, but to have that is one thing and to create a chance is another thing.
"That's why we have to be there so many times, so many times, so many times and you're hoping that one time can then be enough - and it was with Diogo's goal."
On Jota's goal, Slot admitted: "Very pleased. He was close to it already in the first half; I think it was after seven or eight minutes. It was not a surprise they blocked that shot because they are defensively an incredibly strong team. For him to come up in the second half, he had two of these moments as well and the other moment was blocked.
"But (for the goal) he found just a bit of space and he scored the goal, which was nice for him but nice for us - and by us, I mean his teammates, the staff and the fans."
Meanwhile, Slot was left unimpressed with Everton defender James Tarkowski escaping a red card for his challenge on Alexis Mac Allister in the first half.
He insisted: "Let me first say that I don't want to comment about the situation because so many people already commented on that, even people that are not liking Liverpool a lot, and they were all so clear and obvious what the decision should have been. There's no need for me to comment on that. Was I surprised? No."