Wales were on course to win their first game on Australian soil since 1969 - until replacement fly half Mike Harris stroked over a penalty with the last kick of the match to deny Warburton and his brave troops a rare southern hemisphere super power scalp.
"Speechless, absolutely demoralised to come so close," he said immediately after the game. "It's tough when they get momentum on the line-out and you have to stop it. Just gutted.
"It was very physical. We've showed a lot of character all season, it's just getting that vital win out here. I don't think you can get any closer than that to be honest. We have to pick ourselves up for next week."
Warburton added: "Now when we do take a lead we've got to capitalise on that and not let Australia back into game. We are desperate to get a result out here and this sill motivate the boys even more."
Australia captain David Pocock paid tribute to the battling Welsh performance, "Credit to Wales, that was a tough game out there," he said.
Wales caretaker coach Rob Howley was proud of his team's efforts despite seeing his team unable to close the game out.
"We were quite clinical when we had the ball and took our opportunities, but we just gave them one too many opportunities to get that kick at goal with discipline in certain areas," he said.
"I said to guys they could take great heart from their performance. I thought we defended well, the first half in particular when we needed to. We got off our line very quickly and made our tackles. In the second half through our defence we got our try and in just two minutes probably toward the end made a couple of wrong decisions and it's cost us the game.
"We'll be better for that but it's hard to swallow. In international rugby there's a fine margin between winning and loses. For 79 minutes and 20 seconds we've done a lot right."