Australia are unlucky to have a very tough route to the finals. Their previous non-appearances reflect that.
They had to beat extremely strong teams in play-offs since time immemorial. Let's see...
1) For the 1994 World Cup in the US, had to beat Argentina (yes, with Maradona) and failed.
2) For the 1998 World Cup in France, had to beat Iran (which co-incodentially also beat the US team later in the Finals' first round) and failed.
3) For the 2002 World Cup in Japan/Korea, had to beat Uruguay (two times World Cup winner) and failed.
4) For the 2006 World Cup in Germany, had to beat Uruguay (again) but this time they did it.
I don't think the US was ever subject to this type of playoffs.