Chemsdine Talbi had Sunderland ahead midway through the second-half before Liverpool equalised after 81 minutes when Florian Wirtz's shot deflected in off Nordi Mukiele.
Asked if teams now feel more comfortable playing against them, Slot said: "It's clear that teams that play us now think they can get a result. Not only think, because that has been shown this season. And even in the games we've won, they also fuelled the confidence for other teams like, 'Hmm, something is possible' because the wins we had at the beginning of the season weren't easy ones as well.
"I don't completely agree with you that they grew into the game because I think throughout the whole second half there was only one team that had the ball and only one team that was playing on one half. But yeah, if they got a free-kick off the referee or they had a goal-kick, they could bring it to our half with a long ball. And we had to defend three or four times a set-piece and a throw-in and a corner kick.
"And of course, that is a danger with them because they have shown this season that they are a threat in set-pieces. The good thing for us is we didn't concede from a set-piece. Maybe as a result, we got at least a point."
On changing Cody Gakpo for Mohamed Salah at halftime, Slot
The Dutchman also said: "In my opinion, Cody struggled to dominate the one-v-ones. If you want to have any chance against, like I said, they were pressing high but also in multiple situations they were in a low block, (so) the way to score is quite simple: you need a moment of magic from a player or you need a set-piece to score.
"I felt in the first half Cody struggled to find that moment because it was hard for him to dominate the one-v-one or get crosses in. In the first half we played with (Dominik) Szoboszlai off the right to be defensively strong enough not to concede enough as we did in the last few weeks. I changed it to Mo on the right side and then played with Florian Wirtz off the left."