Hair-pulling is not specifically mentioned in the laws of the game, however it is categorised as violent conduct.
That is because it cannot be considered something you would do naturally when challenging for the ball.
Everton said: "We appealed in the firm belief the incident did not meet the threshold for violent conduct as defined in the rules, and that the action was neither forceful nor intentional.
"Our appeal was also lodged in support of Michael Keane, a player who plays the game with the highest ethical standards and who, prior to Wednesday, had never been dismissed for violent conduct in his career.
"It is our firm belief that the severity of the three-game suspension is clearly excessive, and we are surprised and disappointed that this point of appeal has also been rejected."
BBC Sport has approached the FA for comment.