Tim Cahill opened the scoring for the Socceroos in the 49th minute of Thursday's encounter, a goal that came when captain Zheng Zhi was lying on the ground in the penalty area after a slight coming together with Cahill.
Nobody came in to cover for Zhi, allowing Cahill the freedom to put a bicycle kick into the back of the net, much to the frustration of Perrin.
"Even if you lose concentration for one second, you pay the price," said Perrin. "Before Cahill scored his first goal, one of our players fell to the ground and that virtually cost us the game.
"After the Australian team scored first, their self-confidence grew and that made our situation even more difficult."
However, Perrin said that it was he's team's failure to provide an attacking threat that ultimately cost them.
"I don't think conceding was the (whole) problem," he said. "The problem was that we could not find a way to equalise and how we played the opposition once they scored first. Australia played well, and my team did their best."