Jurgen Klopp and Duncan Ferguson were reportedly involved in a heated argument on the touchline during the Merseyside derby at Anfield.
A first-half goal from Richarlison and second half penalty from Gylfi Sigurdsson gave Everton their first win at their rivals' home since 1999 and condemned the Reds' to their fourth-straight defeat.
According to reports from Anfield, tempers flared between Klopp and Ferguson in the second half following a Liverpool penalty claim, with Toffees' captain Seamus Coleman intervening.
Ferguson was said to have had a big smile on his face after the appeal with Klopp allegedly shouting: 'Why are you laughing?