Although the incident went unpunished on matchday, the FA reviewed the footage and decided to charge Tamas who has now been suspended for three Premier League matches.
Vaughan required plastic surgery to mend a badly-gashed lip and although Tamas says there was no intent to harm, he does concede the action was careless.
"We have spoken at length with Gabriel and he is adamant that he did not intentionally elbow James in the face," West Brom's legal director Richard Garlick told the club's official website.
"However, he admits the way he turned in the penalty area was clumsy and he has apologised to James through a mutual friend for the injury he has suffered.
"We as a club, also send our best wishes to James.
"Although we accept Gabriel's version of the incident, both the player and the club have decided against appealing the decision as it would be very difficult to overturn."