Eddie Jones suggested Darcy Swain's first-half dismissal worked in Australia's favour as England crashed to a dismal fourth defeat in a row.
England initially took advantage of their opponents being down to 14 men thanks to Ellis Genge's try early in the second half, only to then collapse in remarkable style.
Jordan Petaia, Folau Fainga'a and Pete Samu crossed over to put Australia out of sight, with Henry Arundell and Jack van Poortvliet tries mere consolations for England.
The visitors were five points ahead with 20 minutes left but went on to lose 30-28, and Jones says their terrible final-quarter showing was not helped by Swain's earlier sending off.
"In some ways, the red card can work against you. Sometimes the referee wants to compensate. We didn't adjust as well as we should have," Jones told Sky Sports.
"We had enough moments to win the game. At 14-9 with 20 minutes to go we should have put it away. The reaction from the boys is to win this series 2-1. We have to go again.
"The message at half-time was to keep putting pressure on and we did that in spurts. We lost the ball twice on their try-line and we didn't pressure them, whereas Australia did.
"We need to work on our finishing and a bit on our defence as well. There are still some positives to come from what has been a very disappointing result for us."
Jones clarified at his news conference that he did not blame referee James Doleman for his side's defeat in Perth, but reiterated Swain's exit inadvertently helped Australia.
"You look at the history of the game, whenever you get a red card the referee evens it up. He helps the team with the red card," he said.
"It's social reciprocity, it happens, that's normal and we've got to be good enough to handle it.
"It happens in every game of rugby I've seen. The team gets a red card and the opposition gets evened up. Because they're nice blokes, referees.
"I'm not criticising the referees, I'm not using it as an excuse, that's the reality of rugby.
"I'll say it again. I think when you play against 14 men the referee has a significant impact on the game and you've got to be good enough to understand what that is.
"We weren't good enough to understand what that is and therefore we paid the price."
England's defeat was their first against Australia in nine Tests amid a run stretching back to October 2015, pre-dating Jones' time in charge.
Not only did the home side play more than half of the match a man light, they also lost three players to first-half injuries after Quade Cooper pulled up in the warm-up.
Swain was repeatedly provoked by England's players, with Jonny Hill seen pulling his hair, but Australia coach Dave Rennie is unsure if that was a deliberate ploy from the opposition.
"I'm not sure if it was a team plan, but there was certainly provocation there. Not just in that situation but also earlier in the game," he said.
"We'll have a decent look at the footage and work out how we're going to appeal that. We'll have decent look at the card. We'll be seeking clarity around it.
"We train with the scenario of playing with 14 or 13 players all the time. What we know is that we just have to work harder. We found a way."
Australia have now won their last five Tests on home soil – their best-such run since 2008 – and five of their last eight when hosting European opposition.
The second match in the three-Test series takes place in Brisbane next Saturday, before concluding in Sydney the following weekend.
Real Sociedad 0-2 Real Madrid: Vinicius, Mbappe penalties close gap on Barca
Vinicius Junior and Kylian Mbappe both scored penalties as Real Madrid saw off Real Sociedad 2-0 at the Reale Arena.
Carlo Ancelotti's side moved to within a point of LaLiga leaders Barcelona, who visit fifth-place Girona on Sunday.
Already without the likes of Jude Bellingham, David Alaba, Eduardo Camavinga and Aurelien Tchouameni, Madrid suffered another injury blow in the 24th minute when Brahim Diaz was forced off with a muscular issue.
After a goalless first half, the visitors broke through 13 minutes after the restart with Vinicius slotting home from 12 yards after Sergio Gomez handled Arda Guler's shot.
Vinicus was then felled for Madrid's second penalty, which was awarded following a VAR review, with Mbappe making no mistake in sealing all three points.
Data Debrief: Madrid extend unbeaten streak
Extending their unbeaten LaLiga streak to 37 matches, Madrid have now won four successive away league games against Basque opposition for the first time since a run of four such victories between 2011 and 2013.
By contrast, Sociedad have now suffered four straight home defeats in the Spanish top flight for the first time since 2007.
Bournemouth 0-1 Chelsea: Late Nkunku strike snatches victory for Blues
Christopher Nkunku proved Chelsea's hero as his late strike secured a narrow 1-0 win over Bournemouth in the Premier League.
The forward climbed off the bench to strike the winner five minutes from time at the Vitality Stadium, where Robert Sanchez kept out Evanilson's first-half penalty.
Bournemouth looked the more likely to take all three points in the contest, with Marcus Tavernier's long-range thunderbolt rattling the crossbar early on.
Sanchez then came to rescue on 38 minutes by denying Evanilson from 12 yards, albeit after he had conceded the spot-kick for a foul on the Brazilian.
The woodwork denied the Cherries again after the break, with Ryan Christie seeing his precise low effort hit the outside of Sanchez's right post.
However, it was Chelsea who snatched the points with five minutes remaining. Receiving the ball from Jadon Sancho, Nkunku cleverly skipped away from a couple of challenges before slotting past Mark Travers in the Bournemouth net.
Data Debrief: More happy travels for super sub Nkunku
Nkunku's piece of individual brilliance settled the contest. All four of his Premier League goals for Chelsea have come away from home as a substitute.
The Blues held out at the other end to claim their first away league clean sheet in 18 attempts, while winning four straight matches on the road for the first time since 2022.
Meanwhile, history was made at the Vitality Stadium with the referee showing a total of 14 yellow cards; the highest amount issued in a single Premier League game.
'You cannot switch off for one second' - Silva rues late West Ham equaliser
Marco Silva conceded Fulham "cannot switch off for one second" in the Premier League, after Danny Ings' last-gasp equaliser denied the Cottagers all three points against West Ham.
The hosts appeared on course to take the spoils in the London derby at Craven Cottage, where Raul Jimenez put them in front after 24 minutes.
However, the visitors snatched a dramatic equaliser in the fifth minute of stoppage time, when substitute Ings fired past Fulham goalkeeper Bernd Leno.
And Silva acknowledged his side's brief lapse in concentration proved costly.
"It just shows that in this Premier League, you cannot switch off for one second," he told BBC Sport. "We are aware of the quick throws, and we have to keep focus and concentration.
"A big frustration for us because, before that, it was a good performance. It was clear we were the best team on the pitch. They did not have one shot [on target] in the first half.
"We should have won this game. It was not a game where West Ham pushed us back. The goal came after we switched off. It just shows you have to keep focus until the last second."
Silva also felt Fulham should have been awarded a first-half penalty when Adama Traore was challenged by Max Kilman.
"It was a clear, clear, penalty in my opinion," he added. "It's difficult to understand why it was not a penalty in that situation. I don't even want to say anything more about it."
Meanwhile, West Ham boss paid tribute to Ings, who was making only his second Premier League appearance of the season - with both coming as a late substitute.
"It was a very 'Danny Ings' goal!", Lopetegui told West Ham's official website. "He is always agile in those kinds of actions, and he took his chance very well.
"I'm really happy for him, because he hasn't played much up until now, but he is always ready to go. He is a really good example to all of his team-mates, and it's great to see his work pay off.
"As a player, it can be hard when you don't know when the coach is going to call you. The important thing is to try and always be ready, because you are going to be needed at some point.
"Scoring in the last minute today is important, because he's shown everyone that you have to believe until the end. Even though there were things we could do better today, we kept going, and we got something out of the game."
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