The tactician saw red when screaming in the face of the Fourth Official straight after Napoli took the lead in an eventual 2-1 victory at the San Paolo.
Klopp apologised after the game, stating in a press conference that he “overstepped the mark and it was really pathetic.”
The 46-year-old will sit out his one-match ban for the home match against Olympique Marseille on October 1.
Napoli are in Group F with Borussia Dortmund, Marseille and Arsenal.
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