The Socceroos completed a fairytale tournament by beating South Korea 2-1 after extra-time in a gripping Sydney final.
Substitute James Troisi struck in the 105th minute, blasting home from close range after Korean goalkeeper Kim Jin-hyeon spilled Tomi Juric's cross into his path.
"It speaks for itself," he told reporters after the game.
"All I can recall is everyone who didn't believe in us. That's all I can recall. It's just a sweet feeling to know people are going to have to jump on the bandwagon.
"They've got no choice – we know the people who love football and the people who don't.
"It was a tournament we were never supposed to win with this group of players."
Australia looked like they would win the match in normal time, leading right until stoppage time through midfielder Massimo Luongo's first half scorcher.
However, Korean superstar Son Heung-min stunned Ange Postecoglou's side with a powerful finish to save his team and send the match to extra time.
"We were programmed to go out and play the game and not the occasion tonight," added Cahill.
"The boys did it and it's a massive moment for Australian football.
"I'm really proud of the boss, someone being Australian and having the passion to believe in the youngsters. To believe in the talent to really take us to a different level.
"Tonight is one of the biggest moments in sport for Australia. Because this was an Asian tournament and it was so difficult to win.
"We've opened doors inside this team that people would never have known about. Unless this man [Ange] had shown people.
"I'm just happy he took me on the journey 14 months ago. This is a reward for Australian soccer."
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