Rassie Erasmus' complaints about the refereeing in the British and Irish Lions series opener have been called a "sideshow" by the tourists, while Rugby Australia deemed them "unacceptable".
The Springboks boss posted an unprecedented hour-long video monologue online critiquing Australian referee Nic Berry's work in the first Test.
A Rugby Australia statement condemned Erasmus' actions.
Forwards coach Robin McBryde said the Lions were "really happy" with Berry.
In the video. Erasmus said he recorded it in the hope that South Africa would get an "equal chance" in Saturday's second Test, which will be refereed by New Zealand's Ben O'Keeffe, after losing the first.
"We're aware there's a lot of stuff out there on social media but that's not going to affect anything," McBryde continued.
"That's just a sideshow. Everybody realises [referees] have got a tough job to do.
"We were really happy with Nic Berry last Saturday and I don't think it is going to be any different this weekend."
Erasmus may yet be charged by World Rugby for his actions, with the global governing body saying it would raise the issue with the South African Rugby Union.
Rugby Australia said "there is no place for abuse of match officials in Australian rugby", describing Erasmus' behaviour as "against the spirit and values of the game".
"It is important to ensure public attacks of this nature are not tolerated," the union's chief executive Andy Marinos said.
"We will continue to provide support to Nic at this time, as both his physical and mental wellbeing remain a priority for us."
'Rugby prides itself on rising above' - McBryde
McBryde said questioning referees' decisions is "not really my cup of tea", referring to a trial in the Pro14 Rainbow Cup earlier in the year where captains could challenge an officials' call.
The former Wales international said "traditionally rugby has been able to pride itself on rising above that", and added that players are told not to speak back to the referee "from a very young age".
"Hopefully it [the game] will be a good spectacle and we can forget about what's happened this week," McBryde continued.
Lions full-back Stuart Hogg said the players had not watched Erasmus' video "at all", saying "we've just been concentrating on ourselves and left him to himself".
But the 29-year-old did take time to praise Saturday's referee O'Keeffe, saying he is "one of the best" he has dealt with in his time as Scotland captain.
"He's good at communicating," Hogg said. "That's the reason why a large majority of the games where he's involved are allowed to flow.
"Everybody is entitled to their opinion on referees but they're the ones that run the game and they have a huge amount of respect from us as players. I'd hate to do the job if I'm honest."
'Erasmus is trying to divert attention off players' - Skinstad
Giving a South African perspective, former Springboks captain Bob Skinstad says fans will back World Cup-winning coach Erasmus' move as long as it helps the Boks square the series.
"Rassie's star has been shining bright, we have all seen the story and seen what he has done for South African rugby and South African sport," Skinstad told BBC Radio 5 Live's Rugby Union Weekly.
"I think he is trying to divert the attention off the players during a difficult week for the Springboks after losing.
"I played with Rassie and I think he is a tremendous coach. He has always been an innovator, always been a guy who has pushed boundaries and looked for whatever edge you can get, but so has Warren Gatland.
"They play a media game to alleviate focus off their team, and I think a lot of [South African] fans will be going 'wow, that's a big go you've had there, but this is a war'.
"And all is fair in love and war. Rassie only has one more chance at it to keep his team in this series. They lose on the weekend and it's over."
Referee JP Doyle said it is "unprecedented" for comments like Erasmus' to be made so publicly, but they are not unusual behind closed doors.
"For the last seven, eight or nine years there has been a huge amount of dialogue between teams and referees leading up to games and coming out of games," he said on Rugby Union Weekly.
"A lot of this stuff that is going on goes on behind the scenes normally, so [O'Keeffe] would have this regardless. It's just in the public, that's the biggest change."