Martin O'Neill is the early favourite to replace Giovanni Trapattoni as Republic of Ireland manager.
The former Celtic and Aston Villa manager hasn't worked since being sacked by Sunderland last season.
However, FAI chief executive John Delaney wouldn't be drawn on possible replacements when he spoke to RTÉ Sport.
"I think it’s a time for reflection after a traumatic four or five days," he said.
"A board meeting will take place within the next week at which we’ll define the process, time-scale and job description for the next manager.
"It’s been a difficult four of five days for the Association. When we lost to Sweden it looked then that our World Cup qualification hopes had ended. The defeat last night (to Austria) confirmed that."
Leeds manager Brian McDermott, one of those mentioned as a contender, said today he was not looking to leave his current post.
"One day I want to manage [the] Republic of Ireland," McDermott said.
"But I'm at a fantastic club. I owe them and the supporters. I'm committed 100 per cent."
"It's disappointing for me especially because after missing out on the Euros, I wanted to get to a World Cup" - Seamus Coleman
Meanwhile, Ireland full-back Seamus Coleman has admitted that the failure to make the finals had hit him particularly hard after he missed out on selection for the Euro 2012 finals.
The 24-year-old said: "As professional footballers at the standard some of us are at, we want to be qualifying.
"The lads qualified for the European Championship, we want to be qualifying for major championships.
"It's disappointing for me especially because after missing out on the Euros, I wanted to get to a World Cup, and it wasn't to be."
Coleman has been one of the main beneficiaries - James McCarthy is the other - of Trapattoni's agreement to develop a new generation in showdown talks after the 6-1 qualifier defeat in Germany, which followed hard on the heels of a difficult campaign in Poland and Ukraine.