The Spaniard was asked by the Football Association to explain the gesture, made as he left the pitch at half-time.
After receiving his observations, the FA has decided the 27-year-old will not face any action.
However the FA has yet to decide on the outcome of an improper conduct charge against Costa from the same game.
Costa received a second yellow card after clashing with Everton midfielder Gareth Barry in the 84th minute of the FA Cup quarter-final.
He was charged over his behaviour after being sent off, and has until 18:00 GMT on Thursday to respond to that charge.
The Chelsea player appeared to bite Barry in the incident, although both players have denied that happened.
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Chelsea striker Diego Costa will not be punished for making a gesture to Everton fans during his side's 2-0 defeat at Goodison Park.