Martin, who is known for his harsh stare downs and strong words at times when players make mistakes on the court, said Tuesday he went too far after getting caught up in the moment.
Martin also apologized to fans around South Carolina's bench who heard the exchange.
Martin says there was no place for him ever to speak to Williams like he did. He says he met with and apologized to his senior guard.
Williams had 14 points to lead the Gamecocks in the 75-74 loss to the Rebels. The Gamecocks (7-10, 0-4 SEC) play at Georgia on Wednesday night.
The Associated Press contributed to this report.