As the rugby league community rallied around Inglis, Greenberg defended the governing body's role in helping their stars handle the spotlight of professional sport.
"I'm not sure if you'll ever do enough in order to do the very best job you can," Greenberg said.
"But I would say there's been an extraordinary amount of work done over the last five years, particularly to assist our athletes off the field."
Inglis last week became the latest high-profile player to check into a rehabilitation clinic for personal issues, after the likes of Kieran Foran, Mitchell Pearce and Ben Barba.
Greenberg said it was a reminder that not all players could cope with the pressures of the competition, but believed the game could lead the way in dealing with a social issue.
"It tells you that they're in a very high profile environment with huge pressures, and some of them aren't equipped to deal with the pressures that come with being an elite athlete," he said.
The former Canterbury boss admitted he was surprised to learn of Inglis' struggles, but told players to be unafraid of asking for help when facing adversity.
He said the game could be a trailblazer in erasing the stigma around mental issues.
"I certainly didn't expect it and I think most people would say that today," Greenberg said.
"On the outside, our rugby league players look big and strong and fit.
"The message is simple - not just for our players but the broader community - which is, 'If you're going through some difficult moments, never be afraid to put your hand up'.
"Never be afraid to ask for some help, whether that's professional or just a mate to talk to.
"The message that we would love to send through the profile of the game is, 'Put your hand up when you need help. It's a sign of strength, not weakness'.
"Rugby league can help reduce the stigma for young men to put their hand up when they've got some problems, and clearly that's what Greg's done today.
Unlike the dramas that involved Foran, Pearce and Barba - who all copped suspensions for a differing indiscretions - Greenberg denied the integrity unit was investigating Inglis' case.
"This is an issue where Greg's obviously having some difficulties and he's trying to get the help for that," he said.
"I haven't spoken to Greg directly but I have had very regular contact with the Rabbitohs club and I've been getting regular updates through their staff and we'll continue to do that."