Two goals in two minutes from Ryan Gravenberch and Wirtz had Liverpool 2-0 ahead at halftime before Santi Bueno struck just after the break.
On his £125m signing now getting off the mark, Slot said: "I think I'm quite sure it was a relief for him, this I could see after his reaction after he scored the goal – and the same I saw with his teammates.
"I think they were really happy for him scoring his first goal because in football – rightly so, maybe – we mainly get judged on results and individuals mainly get judged on goals and assists. Sometimes we tend to forget what else there is to do during a game.
"I think he's had multiple good games for us but I also feel he gets better and better every single game he is playing for us. He gets fitter and fitter and was getting closer and closer to his first goal. Then it was not a surprise to me that he scored one today, but he would probably be the first one to understand that one goal is not enough.
"He will score many more goals for us than only this one, but I also liked his performance during large parts of the game today. I think he was special in a lot of moments."
While happy for Wirtz, Slot was less satisfied with the way Wolves fought back after halftime.
He also said: "I think if you go 2-0 up at half-time, you're expecting a different second half than we had to face. But in football a goal can massively change momentum, and that's why I was so, so, so annoyed when the goal at (Manchester) City was disallowed because we were struggling in that game – probably just as much as Wolves were struggling today – but then a goal can make a lot of difference. That's what you saw today – not that after the 2-1 we didn't have ball possession anymore, but it was much more of an equal game.
"Of course you're frightened every time when they do arrive, especially when he brought another big man in, with the crosses they gave. But I don't think we conceded a lot of big chances. I think the first big chance we conceded was, again, a goal – not for the first time this season.
"But for the rest, I saw a team that was fighting to get the win over the line – not with the best possible football but there was a proper fight. And a bit better than last week (in) the last 10 minutes. That wasn't too difficult, by the way!"