Ian Foster and Dave Rennie backed the law change over red cards in the Rugby Championship after New Zealand completed a Bledisloe Cup sweep over Australia on Sunday.
Jordie Barrett scored the game's opening try in Perth, setting New Zealand on the way to a 38-21 triumph that means they have won all three Tests against their trans-Tasman rivals this year.
However, the full-back did not last long after scoring, dismissed for dangerous play after catching Wallabies winger Marika Koroibete in the face with a boot while catching a high ball.
All Blacks boss Foster felt the decision to send off Barrett was a little harsh, particularly as it could lead to a suspension that has an impact on the rest of the Championship campaign.
"I was pretty surprised to be honest [that he got the red card]," Foster told the media. "We'll go and have a good look at it, but certainly we'll be putting together a case for that one.
"He just lost balance and you could see he tilted and you could see what happened.
"I feel for the refs in situations like this, because technically they saw things and they make their decisions. I get all that. Have we got a technique problem? No."
While Barrett did not feature again, the tournament is experimenting with a ruling where players who have been sent off can be replaced by a substitute after a 20-minute period.
The initiative allowed the All Blacks to be back at full strength early in the second half, by which time they were comfortably in charge of proceedings.
"It's why all the SANZAAR countries were pretty united in wanting to carry on this global trial," Foster said of the trial.
"It's easy to ask me my opinion because we were the ones on the end of it, so we probably benefited by only having a 20-minute red card. I get that.
"But we were keen supporters of that even before the game and today probably justifies that."
Wallabies head coach Rennie felt the red card was the right call, even if Barrett had not been malicious in making contact with Koroibete, but also backed the initiative on trial.
The hosts still trailed 18-0 at half-time and while they did cross three times after the break, New Zealand eased clear to claim a bonus-point victory that puts them top of the table after two rounds.
"I think it's good that we have a 20-minute red card at the moment, because it's certainly not malicious," Rennie said.
"But based on law, when you field a ball, kick your foot out and hit someone in the head, there's going to be repercussions for that. So, I think the decision is probably accurate, and the fact it's only 20 minutes is a good thing."