Byrnes was fined $7 500 on Wednesday for an ''unwarranted and serious verbal attack'' on Carter in newspaper comments published in March.
They came after he had successfully appealed a 10-match ban for dangerous play against Carter who had alleged he was eye-gouged by the Russian international during the round-two match at AAMI Park.
Byrnes, who hasn't played since that match due to an elbow injury, has until 4pm today to decide whether to appeal, but it is believed he intends to do so.
SANZAR judicial officer Nigel Hampton found he had committed an ''act of misconduct''.
He said that the interview contained ''an unwarranted and serious verbal attack by Mr Byrnes on the integrity and good character of another player [Carter], an attack such as well might impair public confidence in that other player's character and integrity''.
In the newspaper story, Byrnes said Carter's actions were a ''disgrace''.
''I give him credit as a player, but to carry on in terms of bringing another player down and potentially ruining their livelihood, it is a very poor quality to have as a human being,'' Byrnes was quoted as saying. ''To be falsely accused with such a slanderous tag as Tom has said is extremely poor form.''
Hampton said he gave credit to Byrnes's long and unblemished career, but found there was no remorse shown or apology issued.
He ordered him to pay a fine of $5 000 and $2 500 in SANZAR costs.
Rebels chief Steve Boland said the club had supported Byrnes but any appeal was ''a decision for Adam''.