The Green Falcons crashed out in just the third round of Asian qualifying for the 2014 World Cup in Brazil after they were beaten 4-2 by Australia in Melbourne.
That left former Barcelona boss Rijkaard's future in doubt, although he was unwilling to discuss his next step.
Asked at the post-match press conference what his next challenge might be, the Dutchman replied: "To get home".
Rijkaard, 49, maintained he was keen to remain in charge despite the disappointment.
"It was a game we focused on and it was really important for us. It's a sad moment for Saudi football," he said.
"If you want to come out of a sad moment you have to work really hard. If I continue working there I'll work really hard."
Saudi Arabia reached four consecutive World Cup finals between 1994 and 2006 but have now not qualified for the past two.
Rijkaard's side had looked on course when they led 2-1 with 20 minutes to go, but the Socceroos scored three times in as many minutes to end their hopes in wet conditions at AAMI Park.
Second-half goals from Alex Brosque, Harry Kewell and Brett Emerton were enough for the Socceroos - who had already booked their place in the next round of qualifying.
"I think it (defeat) had something to do with fatigue," Rijkaard said.
"Maybe with the pressure on the players, maybe the equaliser it took away the courage of the players.
"Another thing, the conditions of the field, a lot of players weren't used to the conditions, they weren't stable and were slipping away.
"They were not wearing the right boots. That wasn't in our favour."
With Saudi Arabia beaten, that handed the chance to either Oman or Thailand to take advantage, as they played each other - and it was Paul Le Guen's Oman who booked their place in the next round as they won 2-0.
South Korea avoided being dumped out as they claimed a 2-0 win over Kuwait with former Middlesbrough man Lee Dong-gook on target.
As it turned out, South Korea need not have worried about the result, as second-placed Lebanon lost 4-2 in the United Arab Emirates.
Qatar grabbed a late equaliser against Iran, and the 2-2 draw means they progress at the expense of Bahrain who, despite their best efforts, are out.
Bahrain went into their game with Indonesia needing to make up a nine-goal deficit, and they did their part with a 10-0 success, but they also needed Qatar to lose.
In other games with no impact on fourth-round places, already-eliminated China had a 3-1 home win over a Jordan team that had booked its place in the next stage.
Uzbekistan won 1-0 at Japan in a clash of the top teams in Group C, but both teams were already through.
Tajikistan secured their only point of third round qualifying by drawing 1-1 at home against North Korea but both nations already knew they were out.
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