The clubs have been charged with failing to ensure their players “did not behave in an improper and/or provocative way” after the final whistle.
Liverpool head coach Slot is charged with having acted “in an improper manner and/or used insulting and/or abusive words and/or behaviour” towards referee Michael Oliver and one of his assistants, which led to the Dutchman being red-carded.
Slot’s assistant Sipke Hulshoff, who was also sent off, faces a similar charge for his behaviour both before and after he was dismissed.
The clubs, Slot and Hulshoff have until Wednesday, 19 February to respond to the charges.
The late chaos began after James Tarkowski scored a dramatic 98th-minute equaliser for Everton, which was awarded after a video assistant referee (VAR) check.
Liverpool were adamant the goal should have been disallowed because of a shove by Toffees striker Beto on Reds defender Ibrahima Konate in the build-up.
Everton midfielder Abdoulaye Doucoure celebrated in front of the Liverpool fans at the final whistle before being confronted by Reds midfielder Curtis Jones, with both players sent off for second yellow-card offences.
Slot and Hulshoff were then both shown the red card after approaching Oliver on the pitch.
Reds boss Slot told a news conference on Friday that “emotions got the better of me” and he should have “acted differently”.
The draw moved Liverpool seven points clear at the top of the Premier League, with neighbours Everton rising to 15th and 10 points clear of the relegation zone.
Slot is expected to be on the touchline for Liverpool’s Premier League match against Wolves at Anfield on Sunday (14:00 GMT).
The Premier League initially reported on its website that Slot would be banned for two matches “for using offensive, insulting, or abusive language”, but that was later deleted. It is understood human error was to blame for the erroneous post.
