The 1-0 win, via Diogo Jota's early goal, means Liverpool go into the international break as Premier League leaders.
Slot said afterwards: "Mostly for me it's special.
"Players go to their national team and they think of the national team, but for me if I lose it is three to four days of being unhappy. I think my wife will be happy as she will have someone home who is happy.
"Really satisfied with how we started the season. It is a good start not only the results, but I liked our performance today.
"There was a period of the game we conceded free-kicks and that was a difficult period. For the last 10 minutes we kept the ball very well."
On Crystal Palace's possible penalty call, he said: "The ball is going to the goalkeeper. If he had given this one then VAR wouldn't have changed it. It is not a penalty for me as he (Marc Guehi) wouldn't ever get the ball."
On the fixture list after the international break: "The fixtures are difficult, but I have felt how difficult Wolves and Palace are away. It is good that we have won these games and it is up to us to show ourselves in the big games.
"Unfortunately Alisson will not be with us in these matches with how he walked off the pitch."
On Vítezslav Jaros' debut, who came on for an injured Alisson, Slot said: "Really good. He had a good season and he won the league and cup with the team (Sturm Graz) in Austria (last season).
"He wanted to go (back this season) and have playing time. We said at a club like this we need a good third goalkeeper as well.
"It was a nice moment for him to make his debut for Liverpool."