David Alaba's late goal earned Austria a 1-0 win in Vienna to condemn the Republic to defeat in a must-win encounter for Giovanni Trapattoni's side following last week's loss to Sweden.
The defeat is now set to end Trapattoni's reign as Republic of Ireland manager with their hopes of qualifying for next summer's finals up in smoke barring victories over leaders Germany and Kazakhstan by sizeable margins in their two remaining games and an unlikely series of results elsewhere
The FAI have now issued a statement confirming they will be reviewing Trapattoni's position after a disappointing qualifying campaign. The manager's press briefing scheduled for Wednesday has also been cancelled.
"The recent results against Sweden and Austria were very disappointing for everyone involved in Irish football, the manager, the players and supporters," read the statement.
"Our aim of qualification, although mathematically possible, is now highly unlikely even though the team will always do everything within their power to keep that hope alive.
"The FAI Board of Management will now consider the current position over the coming days."
The Italian though was in no mood to tender his resignation as he was grilled about his position during his post-match press conference at the Ernst Happel Stadion with former Sunderland boss Martin O'Neill a hot favourite to succeed him.
Trapattoni said: "It's for the FAI to decide if they want us to continue or finish our agreement.
"It's okay if they decide to change us all, but until then, we will continue because it's not our decision.
"The FAI will decide what to do, but we have an agreement until May 31 or June 1, I don't know.
"I wasn't joking the other day when I said if I was (FAI chief executive) John Delaney, evaluate what we have done in the last two years and after decide yes or no. It's not my job to do this."
Trapattoni said on the game: "After the first half this evening, I had again the dream to win this game because we have two very good chances with Shane Long and also Robbie Keane.
"Over the 90 minutes, I don't think we played badly, but as the game developed, Austria were a little bit superior.
"But our aim was to achieve third place because after Sweden won, it was not possible to continue thinking about qualifying."
By contrast, Austria boss Marcel Koller can start planning for a do or die visit to Sweden.
Koller said: "We remain in third place - that means we really have to win in Sweden.
"Sweden are going to play against Germany, but nevertheless, if we want to stay in, we have to win."