Franklin on Monday expressed regret about the incident.
“I would’ve liked when we didn’t win the game we could’ve left the field and shook hands and been men of character all of us and walked off the field and do a great job representing our institutions and the conference,” Franklin said.
Richt said he wants Georgia players and coaches to “keep our poise.”
“For me personally, I like it when coaches can walk across the field and shake hands and say good luck next time,” he said.
A Vanderbilt spokesman said the school would have no comment on the suspensions.
AP Sports Writer Teresa Walker in Nashville contributed to this report.