Bissouma, who joined Tottenham from Brighton for £30m in 2022, played for 45 minutes in Spurs’ friendly defeat against Bayern Munich on Saturday afternoon, before posting the video.
“I’ve been in the game for a long time and every time a situation like this arises, I’ve tried to look at them in a couple of different ways,” said Postecoglou.
“One is, there’s a person involved and, in this case, it’s Biss and he’s made a really poor decision.
“There are still sanctions involved, and some of those include education.
“The second part of that is he’s a footballer and he has responsibilities. He has a responsibility to the club, team-mates, our supporters and everyone associated with the club and he’s failed in those duties, so there’s got to be sanctions for that.”
Postecoglou further explained his disappointment at Bissouma’s behaviour.
“There’s the personal ramifications, because it’s illegal,” said the former Celtic manager.
“Then there’s the professional responsibility – the example you set as a professional footballer – because there are so many people who follow the Premier League and we’re all in a pretty privileged position.
“He’s made a poor choice. But within that context, we all make mistakes, there should always be an opportunity there for rehabilitation and redemption for every human being, including footballers.
“That’s up to Biss now.”