The Power have issued a strongly-worded statement after another day of drama involving their forward.
Rioli had made himself unavailable for Port Adelaide's Showdown with the Crows on Saturday night, calling his threatening message to an opponent "unacceptable". He added he was mentally in no state to play.
The AFL later released a statement, saying they were suspending Rioli for one game and requiring him to participate in "education on respectful/non-violent language and conduct".
While the Power accepted the ban, they said the AFL industry can do more to understand what Indigenous and multicultural players and staff go through daily in the game.
"Willie, like many of our First Nations and multicultural players, has endured racist abuse both directly and casually throughout his career - not as exceptional incidents, but as a persistent, ongoing reality," the club said.
"On-field comments that may not seem racial on the surface, can be interpreted as racist to a First Nations or multicultural person who has endured systematic racist comments since they were young enough to recall."
Port added they had written to the league last month after the heated fallout from Rioli's online post about Hawthorn, concerned about how racist incidents had been portrayed - specifically that players such as Rioli had provoked the abuse.
"By framing racist abuse as reactive rather than endemic, we are contributing to a narrative that undermines the AFL's stated commitment to eliminating racism from our game," the club said.
The 29-year-old initially escaped any sanction from the AFL despite sending an intimidating message about Bailey Dale to one of the Western Bulldogs defender's teammates, the day after a heated match in Ballarat on Saturday.
But the AFL decided to probe further after reports emerged of two verbal threats allegedly made by Rioli to a Geelong and an Essendon player.
Rioli and Port football boss Chris Davies met with AFL officials ahead of the Power's training session on Wednesday.
Rioli could return for Port's match against Geelong on May 17 as he would have served the AFL's one-match ban.
"We understand in a competitive and at times combative environment there are exchanges between players on field, but they still need to be in the realms of respect and sportsmanship and that applies to everyone," AFL general counsel Stephen Meade said.
"After receiving the additional information about further threats, we investigated and determined Rioli should not be eligible to play this week and that he undertakes further education around a pattern of behaviour we don't want to see in any part of our game – on or off the field.
Rioli apologised privately to Dale on Monday and again publicly on Thursday.
"With all the stress from this week, I feel it's best for me and the team that I take a break," Rioli said via a statement from Port.
"I again acknowledge that my actions after last weekend's game against the Bulldogs were totally unacceptable.
"I say things from time to time on the footy field in the heat of the moment that I wish I didn't and I'm continuing to work with the club on managing this moving forward.
"It's not in my true nature or character to say those things and I apologise for any distress I cause to individuals or their families."
On Wednesday, Port president David Koch said the club was "incredibly angry" about the situation.
"We've talked pretty sternly to Willie about it and said it's just not on," Koch told 5AA Radio.
"I'm making absolutely no excuse for Willie's private message after the game.
"But you can't mix on-field and off-field comments or it will lead to places people don't want to go."
