The FAI have no inclination to sack the manager after the 6-1 loss to Germany, Ireland's worst ever home defeat, but they will have no option if Ireland don't win on Tuesday and the manager holds on to his position.
Trapattoni claimed he retained the confidence of his squad before bizarrely insisting that "they are doing everything I ask them to do".
He said it would not be impossible to continue to do his job if Ireland don't pick up three points against a team ranked 158th in the world.
"You think it's easy, you thought Kazakhstan was easy," he said, referring to Ireland's last-minute victory in Astana last month. "You have no idea about international football."
His former assistant Liam Brady said on RTE that most managers would expect to be sacked after Friday night's defeat and the disappointment of the European Championships, but Trapattoni insisted that depended on the expectation of an individual country.
He denied reports that the players had met without the manager yesterday but confirmed that he had talked to the squad in the team hotel in Portmarnock on Friday night in an attempt to discover what was wrong and rebuild their confidence. "I'm not holding them back. I have never told them not to attack."
The game against Germany was, he said, "a game where everything goes wrong".
Trapattoni said it was important the players recuperate before Tuesday but even if Ireland dropped points in Torshavn, he would not resign. "There are seven games left," he added.
Yet he conceded that the Faroes match was a game Ireland "must win" and he is expected to make two or three changes, with Robbie Keane hopeful of being fit again. Trapattoni also hinted that Robbie Brady might play more of a role.
Realistically, Trapattoni can't stay if Ireland don't win on Tuesday but he emphasised, in a prepared statement yesterday, that a defeat, even a humiliating one, to Germany was to be expected for Ireland.
"Germany are not our target, Sweden and Austria are our targets. You have to recognise their superiority"
While only the most unrealistic would dispute Germany's superiority, the manner in which Ireland caved in was of most concern, but Trapattoni said he had never stopped the team from playing.
"I asked them again today, 'Have I ever forbidden you from attacking?'. They not answer. I know the answer, the opponents don't allow them to attack. I'm not holding them back."
He insisted he would know if the team had stopped playing for him. "I know this team very well. I can always take its heartbeat."
Ireland have a friendly against Greece in November which will be played in a virtually empty stadium if Trapattoni remains. In a cost-conscious environment, the FAI are aware that the public are losing interest in the side but they will also have to find money to pay off Trapattoni, Marco Tardelli and the fitness coach Fausto Rossi.
If Denis O' Brien continues to fund the appointment, Ireland could look for a high-profile successor, with Rafael Benitez, Harry Redknapp and Kenny Dalglish among the possibilities.