The home fans were incensed in the 13th minute when the Scotland internationalist collected the first caution of the afternoon for an off the ball clash with Sam Woods.
Griffiths appeared to leave a foot in on the grounded Accies player, prompting an angry reaction from the hosts who felt it was a red card offence.
Hamilton's Alex Gogic was also booked for his show of dissent to referee Nick Walsh after players from both sides got involved in a melee.
Speaking on BT Sport, McCoist said: "We clearly have the benefit of watching it seven or eight times.
"Initially, I wasn't too sure. After seeing it again, I think it's a red card. I definitely think there's a stamp.
"I think Griffiths has got the option of turning around and getting away from the incident but gets involved for some reason. He could turn the opposite way but he doesn't, he lifts his right leg and puts it down.
"I'll say one thing to you. Alfredo Morelos [would have got a] red card."
His fellow pundit, former Scotland and Celtic manager Gordon Strachan echoed McCoist's claims, adding: "There's a change of pace when he puts his foot down. Leigh had the opportunity to put his foot out the way - [if there was] VAR, it could have been a problem."