Victory came at a cost for Liverpool as goalkeeper Alisson Becker limped off in the closing stages ahead of a much more testing run of fixtures after the international break.
“We should have finished it off with such a dominant performance,” said Slot.
“If you score the second, you break them mentally, and now all the fans kept believing in a result because it was only 1-0, even though, in my opinion, we were the dominant team.”
The defeat leaves Palace still in the bottom three with just three points from their opening seven games.
Slot’s seamless start saw him become the first Liverpool manager to win eight of his first nine games after beating Bologna 2-0 in the Champions League on Wednesday.
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