Referee Mark Clattenburg is understood to have seen the incident and opted against issuing a caution, meaning there can be no retrospective sanction by the authorities.
The two players had fallen to the ground after a challenge by Spanish international Costa.
"I think it is a clear red card," former World Cup final referee Howard Webb said on television at the time.
"He commits a foul on Martin Skrtel, then there is a little kick. The second action is a clear act of violent conduct. Diego Costa is a lucky boy on that occasion."
(Reporting by Steve Tongue; Editing by John O'Brien)
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