The Oranje were forced to come from behind in the second half as Mile Jedinak put the Socceroos ahead in the 53rd minute, but strikes from Robin van Persie and Memphis Depay fired Van Gaal's side to victory.
"I'm not relieved, because I believe in the second half we played better than Australia," Van Gaal told reporters.
"In the first half they played better, but in the second half we had five, six, seven chances.
"I expected us to win. When [Australia's Mathew Leckie] missed that chance, I said to Patrick Kluivert, 'We're going to win this match.'"