Lions fullback Hugo Keenan scored the match-winning try in the final minute of the second Test at the MCG, after Wallabies flanker Carlo Tizzano appeared to have been illegally cleaned out in the build-up.
Tizzano looked to have been hit high and recoiled holding his neck.
TMO Eric Gauzins and referee Andrea Piardi reviewed Lions flanker Jac Morgan's clean-out but ruled there was no foul play, allowing the try to stand.
Turinui, who played 20 Tests for the Wallabies, was adamant it should have been ruled out.
"The end is a penalty to the Wallabies and the referees were too weak to give it," Turinui said on Nine.
"The referees have got it wrong and it's cost the Wallabies survival in the series.
"The British and Irish Lions lead this series 2-0. It was brave to come back from them, but it is a terrible decision that decides this match."
Ex-England and Lions skipper Martin Johnson took a contrasting view, but former Wallabies captain Michael Hooper agreed with Turinui.
"I can see what the referee's saying but there's a penalty there, whether it's on head, on neck or whether he's going straight off his feet to ground," Hooper said on Nine.
"I would say if that was minute one it's a penalty and it was deserved to be awarded and the try overturned.
"If you're refereeing or judging by the letter of the law, minute one to minute 79 it doesn't matter."
Johnson disagreed.
"I didn't think there was enough there for a penalty that would change the game," he said on Nine.
"You have to be very, very sure to change the game on a ref's decision.
"I thought it wasn't a penalty."
Wallabies captain Harry Wilson was in no mood to discuss the incident when he was asked about it minutes after the match.
"I'm probably not in the right emotional state to talk about that," Wilson said on Nine.
