The 22-year-old was quick to praise the Lions in every department but admitted that Britain and Ireland's elite wanted it more than their hosts following 16 years of hurt in the southern hemisphere.
"We always knew that the team that was going to win was the one that wanted it more. They played possessed," said O'Connor, who played in every minute of all three thrilling encounters.
"Physically, they dominated us - we knew had to be right up there and they were just better than us on the night. We made a lot of half breaks, and we knew exactly how they were going to play, but they won the one per centers.
"It was an awesome game to be involved in, and I haven't experienced that physicality before in Test rugby. I'm just gutted with the result.
"It came down to intent, and they had more of it. They wanted it more than we did. Congratulations to them."
Having raced into a 19-3 lead in the first period, things looked stacked in the Lions' favour approaching half time. But O'Connor's converted score on the stroke of the interval and a brace of penalties from the impeccable Christian Lealiifano brought the Wallabies back to within touching distance at 19-16 just six minutes after the break.
At that point, the momentum was all with O'Connor and co, with pessimists across all four Home Nations fearing the worst all of a sudden. But the Lions dug deep, regained their composure and found something extra just when they needed it most.
"It was a great performance by them, they played the full 80 minutes. At 50 or 60 minutes we had really come into the game and I felt the momentum was shifting our way, but they found a way to turn it," added O'Connor.
"We had a great vibe at 50-60 minutes but a couple of errors and some mis-communication let them back in and they made us pay for it. Every little error we made they jumped on, they turned it into points and kept the scoreboard ticking over.
"The scoreboard blew out at the end, but they played clinical rugby. We tried to suck the juice out of their legs, but they just kept coming at us."