Hiddink said he always kept faith that his team would come back against Croatia after twice falling behind.
In the end the two-all draw was enough to send Australia through to the next round where they will meet Italy in Kaiserlauten on Tuesday, Australian Eastern Time.
"We started sloppy ... it was a terrific free kick and we were one-nil down," said Hiddink.
"But I know this team has enormous mental power to be able to come back. I think in the first half we were dominating the game a great deal of it and then we managed to go on,” he said almost as a matter of fact.
There were wild celebrations across Australia as fans took to the streets honking car horns and setting of flares in praised of the Socceroos magnificent comeback.
Howard congratulates Socceroos
Minutes after the game ended Australia's Prime Minister, John Howard, was on the phone to Football Federation Australia boss John O'Neill to congratulate the team.
"I just got off the phone from the prime minister who stayed up and watched the match," O'Neill told ABC radio.
"He just thought it was one of greatest efforts he's ever seen from an Australian sporting team and just wanted to express the gratitude of the nation."
It was Harry Kewell’s stunning late equaliser that secured the draw in one of the most soccer matches of the tournament.
Kewell's 79th minute goal in its deciding Group F match gave Australia the draw it needed to advance - the second time the Socceroos had fought back from a goal down.
A diabolical goalkeeping mistake from Australia's Zeljko Kalac for Croatia's second goal looked like handing the Croatians the win they needed to advance.
Kalac, surprisingly selected by coach Guus Hiddink instead of regular first choice Mark Schwarzer, made a meal of an innocuous long-range shot from Niko Kovac, letting it bounce off his hands over his body to give Croatia the lead.
Penalty controversy
Australia was also denied two clear penalties, while Croatia's Dario Simic and the Socceroos' Brett Emerton were both sent off late in the game after picking up their second yellow cards.
English referee Graham Poll may have had some questions to answer had Australia not advanced, with Mark Viduka denied a clear penalty inside the first 10 minutes when Croatia's Joe Simunic rugby-tackled him in the box.
Then Tomas clearly punched the ball away inside the box again two minutes prior to Kewell's goal.
Poll will also have to answer questions over why Simunic was not sent off in injury time after being shown a second yellow card.
He was allowed to remain on the pitch for a tense final few minutes as Croatia searched for a winner.
Simunic was eventually marched on the final whistle for his third yellow card, but by then the Australians were celebrating.