Cahill's opening goal instantly entered Socceroos folklore: a perfectly executed overhead scissor-kick.
"It's instinct. The World Cup [goal] was probably a fluke like people are saying, and that is probably a fluke again," he said with a hint of sarcasm.
The 35-year-old then sealed Australia's win with another goal, a trademark header.
"As old as I am, I keep hearing the same story about when I'm going to depart ... after tonight, it will probably be a couple of weeks before they say it again," Cahill said.
Coach Ange Postecoglou suggested the best might yet be to come from Cahill, the Socceroos' all-time leading scorer with 40 goals in 81 games.
"I don't need to add anything to Tim Cahill's career. It's spelt out pretty clearly for everybody ... the best may be ahead of him still," Postecoglou said.
But Cahill reckoned he was just a product of being "in an environment where you're valued as a footballer".
"And I still know I can change games," Cahill said.
"I still know I can write my own script and at the same time affect football in a big way in Australia because I have never ever once not believed in the national team jersey."
The buoyant Socceroos yesterday headed to Newcastle, the venue of their semifinal on Tuesday.
Socceroos coach blasts his critics
The Socceroos coach says his biggest challenge is making sure media "crap" doesn't seep into his players.
Ange Postecoglou launched an extraordinary attack on coverage of the Socceroos after his finest moment as national coach, a 2-0 Asian Cup quarter-final triumph over China.
"The only challenge I see is making sure the players don't limit their potential by listening to a lot of the crap that comes in from the outside," he said.
Postecoglou was frustrated at "continually having to say the same story".
"People can't see what I see," he said.
"I think the supporters do, I think the fans are understanding that this is an exciting team.
"Mat Ryan, Trent Sainsbury, Jason Davidson, Mathew Leckie, Mass Luongo are all 22, 23 years of age and they're putting in enormous performances.
"My only concern is that I hope none of them get infiltrated by some of the garbage I read and hear on the outside."
Postecoglou bristled at some pre-match media pondering the fall-out if Australia lost to China.
"I mean, for people to be talking about what happens if we get eliminated tonight -- I mean, seriously," he said.
"We started out on something 14 months ago and I reckon we have stuck to that plan.
"I will be held accountable if we veer away from that plan. But we have stuck to that plan and we're delivering."
- AAP
