Based on SEC rules, any penalty -- from no punishment to a suspension -- will be decided by South Carolina subject to the league's approval, SEC spokesman Charles Bloom said.
South Carolina spokesman Steve Fink said the punishment was up to Gamecocks coach Steve Spurrier. Fink said Spurrier was unavailable for comment Tuesday afternoon, and Spurrier was not asked about the incident earlier in the day at his weekly press conference.
Spurrier's next media availability is Wednesday's SEC conference call, Fink said. South Carolina (No. 7 BCS, No. 9 AP) visits Florida (No. 2 BCS, No. 3 AP) on Saturday in a matchup between the SEC East's top two teams.
South Carolina defensive line coach Brad Lawing told The State in Columbia, S.C., that he was unaware of the incident and had not seen the punch during his film study. Lawing also told the newspaper he hasn't seen video of the punch on YouTube, but defensive tackle Byron Jerideau said he saw the incident.
"It happens a lot," Jerideau told The State after Tuesday's practice. "The refs don't see everything. Hopefully, he won't do it again."
The incident occurred on LSU's first offensive possession of the Tigers' 23-21 victory over the Gamecocks last Saturday. Lonergan blocked Quarles to the ground, then Quarles rolled over on Lonergan. Quarles stood up and punched Lonergan, who was lying on the ground, in the facemask.
There was no penalty called on the play. Bloom said the NCAA requires conference review following specific fouls.
"The SEC has been diligent in reviewing plays that by rule involve the initiation of contact and targeting defenseless opponents to the head and neck area," Bloom said in a statement on the SEC's behalf. "The conference maintains constant communication with head coaches on matters of penalty violations during the season. In the first instance discipline for violations involving non-NCAA-required automatic conference review are to be handled by the institution subject to the approval of the league office."
Quarles did not practice Tuesday due to a shoulder sprain suffered against LSU.
Brett McMurphy covers college sports for ESPN.com.