The flashpoint in question came on January 13 after an off-the-ball trip by West Brom's Claudio Yacob, who had already been booked, on Chelsea striker Diego Costa.
The Baggies midfielder avoided a second yellow card and a dismissal before being promptly substituted by boss Tony Pulis in the 2-2 draw.
Chelsea have been fined £65,000 and West Brom £35,000 and both clubs have been warned about their future conduct for breaching FA Rule E20(a).
A few days after the incident, Chelsea interim boss Guus Hiddink said Yacob should have been dismissed and was so frustrated with the performance of referee Anthony Taylor that he expressed his concerns to fourth official Jon Moss.
"I told him: 'This is one of the worst referees of the Premier League I have experienced'," said Hiddink, who had a prior caretaker spell at Chelsea in 2009.
"He said to me 'you haven't seen me yet', which was a beautiful remark I think."
