Wright on Friday responded to White's claims in an extended radio segment on SEN, where he revealed he made an apology to White in their final conversation before he left the club.
The 36ers have responded to White's claims by confirming the club will investigate the accusations against Wright and senior figures in the team.
The Adelaide co-captain posted a bitter tirade at his former coach on Twitter, suggesting the coach's attitude was responsible for the team's broken culture.
"I've been told to shut my mouth & it will be handled for weeks," White tweeted on Friday morning.
"Well it's now getting out of hand and I won't stand for my teammates getting belted in the media.
"You rise as a team and fall as a team!
"That's a winning cultures MOTO, every time it's been the players. Spare me!"
"8 weeks ago we sat in a team meeting...we were told "if we don't make playoffs, people won't think it's because I'm a s*** coach, they will just think i had a s*** team"...another video session another meeting.
"This time "we have too many empath's [sic], too many guys soaking others emotions. Too many guys that care about their teammates situation and not worrying about themselves. I'm not built like that, I'm the opposite of an empath!"
"Google that and see what man is coaching this club.
"Still the guys shut their mouths and show up to train, play and do their jobs. All while copping this day in and day out....did any of the other coaching staff, 'High performance team' or office staff do anything. NO!!!! is the simple answer.
"Another game day another inspiring pre-game talk....this time 'a racial divide' has split the group and we don't function together. "if you don't want to do it for your teammates go get 30 for yourself and then maybe you will help us win a game" Gee way to inspire young men!
"If you think this is something that has taken place over night... you're dead wrong!
"I'll leave you with a message to our coaches group. A message from our 'high performance manager' about guys 'Well-being scores' WELL-BEING let that sink in and then read it."
White also posted a screenshot that he claims shows Wright posting to the a team group chat where he vents about his players, saying: "F*** all of them. Hopefully it gets low enough for them to hang themselves. F***ing d***s".
Wright, 51, appeared to label White "weak" and suggested a former 36ers assistant coach was the source of his WhatsApp leak when responding to White's claims on radio.
Wright also said he does not expect to hear from the 36ers during the team's investigation into White's claims.
"The departing has nothing to do with Kevin's comments," Wright told SEN.
"It's just an opportunity, now that I'm not the coach, for anybody weak out there to come at me because I really don't have a voice or a stand to anything any more. I'm just a regular Joe now at this point in time."
He did not deny he sent the message White has accused him of posting, but is adamant the screenshot has taken his comments out of context.
He says the betrayal of having his private messages leaked to the public shows the "dysfunction" he was dealing with while trying to lead the team.
In an extraordinary development he suggested he has his own dirt on 36ers players from group chats that they are part of – but says he would never betray them, despite his messy exit.
Wright said he could make every Adelaide player look like an "idiot" if he chose to share some of the private messages they have shared. He says releasing other people's private messages is something he will never do.
"My exit conversation with Kevin White was actually all about apologising to him for putting him under tough circumstances," Wright said.
"I expected him to come in here and be a leader amongst this team and he kinda stood back. If I told the public, the media the reasons why he stood back, he wouldn't look that great. But I'm not going to do that. I'll never, ever, ever betray a player's confidence or another coach's confidence. What they say to me will always stay with me. What Kevin has said to me will stay with me, even though he's already done that to me.
"It's just disturbing that somebody would go in there, take a private message out of there and take it out of context.
"It was absolutely wrong to say. But it was only joking and for them to take it out of context, just shows you the dysfunction that I was dealing with this year."
White's claims have stunned the league and caught the 36ers on the back foot.
The team issued a statement on Friday morning to announce it is treating the accusations seriously.
"The Adelaide 36ers are investigating comments made in tweets from co-captain Kevin White," the team said.
"The club takes the allegations seriously and will investigate further as part on an ongoing review. No further comments will be made until the conclusion of the review."
The NBL also released a statement on Friday to confirm league officials are also treating the accusations seriously.
"The NBL is aware of comments made by Adelaide 36ers co-captain Kevin White on social media today," the league said in a statement.
"The league takes the matter very seriously and is working closely with the Adelaide 36ers and the Australian Basketball Players' Association to seek further information."
Wright on Thursday further hinted at the relationship breakdown with his players, admitting it was time for him to move on.
"To get away from that situation is for me, health-wise, the best thing to happen," he said, according to The Adelaide Advertiser.
"As far as mental health, dealing with the pressures and stresses of that situation.
"I'm just concerned our values were inconsistent with one another and not that mine were right and theirs were wrong, but they were inconsistent and we just weren't heading in the right direction.
"The ones who it wasn't good with, it wasn't good. I'm not a halfway person, I can't be lukewarm, you're either with me or against me and there were four who weren't really committed and by then the three imports and Harry didn't give us what we needed. That was the reality of it," Wright said.
"I would have loved for those guys to be a little bit more driven but we weren't on the same page, and that's not the club's fault, that's my fault and I tried everything I could to get them on the same page as everybody else."
But the 51-year-old believes the 36ers are in better shape than when he joined in 2013.
"I feel like I have left the club in a better position than when I first arrived and I look forward to my next coaching challenge," Wright said in a statement on Wednesday.
Wright coached Brisbane from 2002-08 and also was at the helm of Gold Coast Blaze from 2009-2012.
He was named the NBL's coach of the year in 2004, 2007 and 2017, when Adelaide were beaten in the championship series.
