Slot was shown a red card by referee Michael Oliver for using "offensive, insulting or abusive language," the league said on its website on Thursday.
The 46-year-old Dutchman will be banned for Liverpool's next two games at home to Wolverhampton Wanderers on Sunday and at Aston Villa on Wednesday.
Slot has already served a one-match touchline ban this season, sitting out Liverpool's League Cup clash with Southampton after being shown his third yellow card of the season during a 2-2 league draw against Fulham.
Liverpool assistant coach Sipke Hulshoff was also shown a red card during the post-game mayhem, meaning neither was permitted to speak to media after the match.
Everton's Abdoulaye Doucoure and fellow midfielder Curtis Jones of Liverpool also picked up red cards in the post-game melee sparked when Doucoure celebrated James Tarkowski's equaliser deep in added time in front of the away supporters.
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