Midfielder Essien was shown a red card by Andre Marriner after lashing out at Miller in injury-time of the Blues' victory.
Miller said: "He has clearly swung an elbow or something and he has caught me in the face.
"You cannot do that. I could have gone down. I have seen their lad rolling around earlier from a challenge but that is not in my make-up.
"I am just pleased the referee made the right decision because it should not take me rolling around to send him off."