The Green Falcons crashed out in just the third round of Asian qualifying after they were beaten 4-2 by Australia in Melbourne.
That left the former Barcelona boss' 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.
"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."