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.