The match finished 2-2, with a brawl being sparked at the end of the game. Everton midfielder Abdoulaye Doucoure and Liverpool's Curtis Jones were sent off, with Reds manager Arne Slot and his assistant Sipke Hulshoff also being dismissed.
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.
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 his red card.
Hulshoff 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.