New York Red Bulls forward Cahill levelled Arjen Robben's opener with a sensational volley - a certain contender for goal of the tournament - and Ange Postecoglou's team led through a second-half Mile Jedinak penalty.
Strikes from Robin van Persie and substitute Memphis Depay secured a second Group B victory for the Dutch but, as in their opening loss to Chile, Australia won deserved plaudits despite defeat.
"It was an amazing performance," Cahill told television reporters. "I think overall we knew this was our chance.
"We watched a lot of videos of them, we thought that we could win this game.
"From the start we set out to press them high, really let them know that they're in for a game and to play football.
"It's probably one of the unique moments for us in Australian football because we'll earn a lot of respect from today's game."
On his fifth finals goal, spread across three tournaments, Cahill acknowledged he had produced an iconic World Cup moment.
"It's a great moment," he said. "The ball was sitting beautifully for me to either chest it or head it back.
"But if you want a shot at the title you've got to have a go at those. It just felt so right to hit it and I hit it sweetly.
"That's what it's all about - defining moments, another one in my career that I'm really proud of.
"Everyone dreams of playing on this stage and I want to leave a mark for all the kids back in Australia and around the world to be inspired by this today."
Cahill unfortunately made it two yellow cards, along with two goals in as many games in Brazil.
It means he will miss Australia's final group game against Spain, but the former Everton man has no regrets.
He added: "It is what it is, I leave everything on the pitch. If we'd got something out of the game today, I'd have been fine.
"I've left everything on the pitch the last two games that I've played and that's what you've got to do; you've got to put your body on the line and sometimes you miss games.
"This has been an amazing World Cup campaign for us but it's not over yet. We will really try and test ourselves against one of the best in the world."
