Dave Rennie says he is "bloody angry" about New Zealand cancelling the teams' Bledisloe Cup match without telling the Wallabies.
New Zealand will not travel to Perth for the 28 August fixture because of Covid-19 restrictions.
New Zealand has announced a snap lockdown after the country's first positive Covid case in six months.
"I'm bloody angry. Our boys all found out through social media," said Rennie.
"I thought 'New Zealand Rugby didn't even have the respect to consult Rugby Australia about their decision', so that's hugely disappointing.
"I feel like there's only one of us doing what's in the best interest of the game.
"Last year, we went to New Zealand to ensure the games were played for the benefit of both countries.
"We quarantined in Wellington for two weeks. The expectation was we made a commitment to go there this year, they'd come here and they haven't honoured. It tells you more about them than us I reckon."
Meanwhile South African Rugby has confirmed it has offered to host the remainder of the Rugby Championship, pending government approval, as competition organisers scramble to find new venues for cancelled matches in Australasia.
Media reports on Friday suggested the competition could be shifted to the northern hemisphere after New Zealand pulled out of hosting two games against South Africa, also confirming they will not honour their next fixture against Australia that had been scheduled for Perth on Aug. 28.
"We have advised SANZAAR that we are ready and able to host the remainder of the competition in South Africa, pending our government's approval," SA Rugby chief executive officer Jurie Roux said.
"We are now well-versed in turning on rugby tests within the prevailing COVID restrictions and have the venues and accommodation necessary. We just need the go-ahead."
South Africa recently hosted the British & Irish Lions for an eight-match tour, including three tests, that was not without incident as both teams had players and staff test positive for the virus.
The Springboks are currently hosting Argentina in the opening two matches of their Rugby Championship campaign, with the second of those fixtures tonight.
The teams were then due to share a chartered flight to Australia to start that leg of the competition, but for the moment it is destination unknown.
-BBC/Reuters