MELBOURNE captain Max Gawn says he is embarrassed by the restaurant fight between teammates Steven May and Jake Melksham that resulted in May being suspended for the Queen's Birthday blockbuster and Melksham requiring hand surgery.

Melksham and May, both 30, fought after drinking alcohol while having dinner with teammates at Entrecote restaurant in Prahran on Sunday night, leaving the Demons "deeply embarrassed".

May received a one-match ban from the club for drinking while in the AFL's concussion protocols and apologised on Tuesday.

Melksham wasn't suspended but won't be available for selection either due to having hand surgery to clean up an infection suffered in the fight.

Gawn said the situation had started with "hurtful banter" and turned into the "horrible act" of "wrestling at a restaurant."

"I'm not gonna lie, I've been embarrassed the last two days," Gawn told reporters on Wednesday.

"I've come out quite frequently and very frequently ... talking about this sort of stuff, how we speak to each other, and almost praising how we've been doing it as a group.

"And we've had a setback here."

Gawn said Melksham had called him on Monday morning, followed by May.

He believed giving both players community service duties was the right punishment for the fight, as they needed to "give back" to their local community.

"It was flattening (to hear the news)," he said.

"We're role models in society and acting like that obviously at a restaurant, and a pretty popular restaurant ... it's just a bad example definitely.

"Those two boys are very remorseful in what they did. But in the end, violence is not the answer, violence is never the answer.

"Yes, it's a horrible act, wrestling at a restaurant in the public, both being well notable people in the community, that's a horrible act.

"But they can give back to community service, they can give back to the community and work their hours through there."

Gawn dismissed rumours May had jibed that Melbourne would have lost year's Grand Final had Melksham played, but conceded there was other distasteful comments.

"The one (rumour) that has gone out is completely false," he said.

"The Grand Final one's completely false and I do want to get it out there because that looks bad on characters. That wasn't said and I'm pretty comfortable and trust those two boys that that wasn't said.

"But there was some other hurtful banter that was there. I'm not going to go into that. That (banter) is something that we've tried to stamp out."

Gawn admitted he was disappointed the other players at the restaurant hadn't stopped May from drinking but stressed the buck ultimately stopped with the 30-year-old.

"It's certainly disappointing that there was a group of six or seven there and Steven was drinking with them," he said.

"I've spoken to all parties involved, and especially the five guys outside of Steve and Jake and I expressed my disappointment.

"Obviously it's a difficult situation at any time. The guy's one of the older leaders in the football club, but we expect our young guys to be able to lead as well and that really was disappointing."

Melbourne football boss Alan Richardson had earlier said the reigning premiers were "deeply embarrassed" and allowing disagreements to "escalate to a physical level is completely unacceptable."