"Fortunately, he's out now even if he's under contract. He's never going to play with my team, never," Di Canio told BBC Wiltshire.
Former QPR forward Clarke, 26, had only been with the club 11 days when the incident happened.
It started on the pitch when Clarke got into a disagreement with fitness coach Claudio Donatelli and as Di Canio appeared to try and diffuse the situation, Clarke and his Italian boss started to row and it continued into the tunnel.
"I discovered that two days [before the game] he asked to leave. I didn't know that before because I wouldn't play a player in a Swindon shirt who asked to leave.
Di Canio and striker Clarke clash after Swindon's defeat by Southampton
"He doesn't deserve to wear a Swindon Town shirt in front of the fans."
He had struggled for form at Rangers and at previous club Sheffield Wednesday, and spent much of his time on loan.
With Clarke likely to be sent out on loan
when the window opens next week, Di Canio, whose Swindon side have not won in the league since the opening game of the season, said he is now keen to move on from the incident.
"We have to go through this moment and then we will be OK," he added.
"I hope he can find a club because as a man I know that everyone can make a mistake."
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