A measured Cheika, whose Wallabies begin their Rugby Championship campaign next month, took his time before responding with his thoughts on the incident.
"Obviously, I have a big gag on my mouth on what I can and can't say, but I know I haven't seen many head-high tackles 30cm from the ground," Cheika said.
The decision was sent upstairs to the television match official before on-field referee Craig Joubert made the final call.
"I think the referee, he was a bit dubious, but the linesman was very adamant, so I think he took his advice.
"That's the way they operate as a team of three, so the decisions were made like that and we've just got to live with it.
"But let's also be mindful of the fact that yes, those decisions went against us, but the key areas where we needed to exert pressure - that being the lineout and the ball from the lineout - we weren't able to manage."
Highlanders co-captain Ben Smith had no doubt the right call was made.
"I have seen it right throughout Super Rugby. If a guy comes in with a swinging arm like that and cops someone on the head, then he has to be taken out of play," Smith said.
"If you take him out of play, Patrick Osborne scores that try. So I had no doubt that was a penalty try."
In the end, the Highlanders scored five tries to one and the result would have been worse for the Waratahs if Lima Sopoaga had not missed a couple of penalty goal attempts and two conversions.
Ben Smith missed his one shot at goal. AAP
