The Reds, who are top of the Premier League by two points from Arsenal, won 2-1 at Anfield on Sunday.
Klopp was effusive in his praise for De Zerbi pre-game and repeated the trick after the match.
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"I told De Zerbi to keep turning the football world upside down," Klopp told BBC Radio 5 Live when asked what they had spoken about.
"I will watch it from some distance. I respect so much what he's doing."
"It is incredible what he has done," added the German.
"Brighton have lost Alexis Mac Allister and Moises Caicedo, they have lots of injuries, but he puts a team like that together. An incredible job."