The Group B rivals played out a thrilling contest in Cuiaba, Chile ultimately just having too much for a dogged Australian side, who fought back from conceding two early goals.
Cahill himself headed Australia back into the game before seeing an equaliser ruled out for offside in the second half.
He said: "There was an incident where the left-back elbowed me and kicked out at me when I was trying to run past him for a cross, and I've got the yellow card.
"I called him a cheat and he said, 'Yeah, I'm a cheat, so what?'
"I said to (Arturo) Vidal, 'This is no good, this needs to be out of the game.'
"They sensed it, everything started turning into grappling, everything they did started to slow the game down and they were getting a lot of free-kicks in their favour.
"It's fine, because this is a great learning curve for this team and what we're trying to do."
