The Blues went on to lose the match 3-1, adding further pressure onto the players and coaches' shoulders.
Following what initially seemed a fair battle between two players, replays soon showed Costa to intentionally kick out at his opponent. Skrtel, to his credit, held back from retaliating, with the general consensus being Costa should have been dismissed for his actions.
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Referee Mark Clattenburg, however, did not see the full extent of the misdemeanour.
This is far from the first controversial incident Costa has been involved in, of course. He was involved in a clash with Arsenal defender Laurent Koscielny during Chelsea's victory against the Gunners in mid-September, also colliding with Gabriel Paulista and playing a part in getting the Brazilian sent off.
Following Chelsea's win - the undoubted high point of their season so far - even teammate Kurt Zouma accused Costa of being a cheater.
“Everyone knows Diego and this guy likes to cheat a lot and put the opponents out of his game, and that happened in the game."
The FA, aware of Costa's latest misconduct, may decide to implement a three-game suspension on the Spain international plus an additional game for this being his second offense in just over a month, reports ESPN.
Former referee Howard Webb spoke to BT Sport regarding the incident, and said: "The FA will have a look I think. I think it is a clear red card.
"He commits a foul on Martin Skrtel, then there is a little kick.
"The second action is a clear act of violent conduct. Mark Clattenburg is pretty close and is in a good position and it's difficult to say that he hasn't seen this."