Spurs had Xavi Simons and Cristiano Romeo sent off as Liverpool won 2-1 thanks to a brace from Hugo Ekitike. Richarlison had given some hope when cutting the lead, though Romero's late dismissal played into Liverpool's hands.
The Reds now sit outside the top four only on goal difference and Slot said: "Of course we are happy with that. But when we started the season, it wasn't as if I was thrilled and completely happy when we were top four.
"We're always aiming for the best possible and, after a very good start we had, we were disappointed with the run of results we had afterwards. But I think you've said it, we are now maybe on equal points for top four, I don't exactly know. But don't forget, in the Champions League we've done quite well with a very difficult draw.
"I see a lot of teams that hardly have a point but we haven't faced them. So, I think it's never been as bad as people said, but it's also true that we are definitely not perfect yet. But we knew this when we made so many changes in the summer that it would take time. Maybe because we won the first five or six games, everybody thought this would just go so easily.
"But as a club, ownership, Richard (Hughes), Michael (Edwards), all the other people, knew that change could, could, could also go with different results – and that has shown to be true."
On Simons' dismissal, Slot added: "I don't think he had any intention to do it. But if you see it back, where he touches him from behind, studs, the height, I think it was calf, (on the) Achilles, already a few times when other teams made fouls like that against us it didn't lead to a red card, but this time it did.
"I've seen multiple times that these fouls are a red card. But I've seen this season a few times when other teams made these same fouls against us that it wasn't."