Wallabies full-back Kurtley Beale was sin-binned for a deliberate knock-on after 22 minutes, with Australia briefly reduced to 13 players with number eight Rob Valetini having received an earlier red card following a dangerous tackle on Wales lock Adam Beard.
Australia head coach Dave Rennie was furious after the final whistle, telling Amazon Prime Video: “I thought some of the decision making by the officials tonight was horrendous and played a big part in the result.
“Kurtley Beale got sin-binned for slapping the ball down. They do the same thing, and it clearly goes forward and they get seven points out of us.
“I am obviously really disappointed with the result. We will end up getting an apology next week, but it won’t help the result. I thought we deserved better.”
But Pivac countered: “I don’t think it (Tompkins incident) is a knock-on personally, nor did the referee, the TMO (television match official), the touch judges or anyone in our coaching box.
“It just goes to show that you can’t switch off and stop. You’ve got to play to the whistle. You tell that to five-year-olds. We were pleased with Nick’s efforts there.
“At the end of the day, we can talk about red cards and yellow cards, but pressure creates cards and we are good enough to create pressure against sides.
“The red cards, I don’t know that we should be explaining that as we don’t give too many away, but opposition have and they need to have a look at that.”
Valetini’s red was the sixth time this year in 12 Tests that an opposition team have had a player sent off against Wales.
Wales recorded a third successive victory over Australia as they ended their Autumn Nations Series campaign in dramatic fashion.
Substitute Rhys Priestland’s penalty with the final kick of a frantic game thwarted Australia and sent a 68,000 Principality Stadium crowd wild.
Hooker Ryan Elias and centre Nick Tompkins scored tries for Wales, yet it was fly-half Dan Biggar’s goalkicking that proved the difference, as he amassed 16 points through four penalties and two conversions, until Priestland struck.
Australia, desperate for a win following losses to Scotland and England, made injury-hit Wales fight every inch of the way despite the numerical disadvantage, as wings Andrew Kellaway and Filipo Daugunu touched down, with scrum-half Nic White also scoring.
James O’Connor booted two penalties and two conversions, yet his conversion attempt of Daugunu’s late score hit the post, and Wales could breathe a huge sigh of relief, despite Beale’s 78th-minute penalty.
Pivac added: “It was a game I felt we should have run away with in that last 15 minutes and made it comfortable for ourselves.
“I was very pleased with the group we had out there in the last quarter of the game. They managed to salvage a result in the end.
“When the dust settles, we will look back at the squad we have used, the depth that we’ve created. When we go one to 15 on our depth chart, the benefits will lie there, really.
“Internally as a group, we will celebrate for the first time in a number of months.
“To come out with a win, no matter how it comes, we are just pleased to get that result today. To fall behind and then to get it at the death, we probably made 68,000 people, and everyone watching at home, pretty happy.
“Development has been the key, and it has been forced upon us in a lot of areas and we’ve gone a bit deeper than we would have liked to.
“There are so many good stories here in terms of the development side of things. It sounds like I am just harping on down that track, but it’s factual.”
Wing Louis Rees-Zammit followed Beard in making an early exit, going off just after half-time, and Pivac said: “Adam has got a bit of a shiner and a swollen side of his face. He took a very big blow and couldn’t play on.
“Louis got a whack to the patella tendon. Hopefully, it’s not going to be too serious.”
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