The pressure on the Italian, who has already admitted that he does not expect to continue beyond the current campaign, is sure to intensify in the wake of Tuesday's 1-0 defeat
The 74-year-old's fate has surely been sealed with his employers under increasing pressure to act after a turbulent twelve months and another unsuccessful qualification campaign but Trapattoni insists he and assistant Marco Tardelli deserve another two years in charge.
"It's not up to me, I didn't announce our jobs. Now it's up to the FAI to make the decision but I say give us the opportunity to continue for the next campaign." he told RTE after the game.
"It depends on what they [FAI] decide but I'm sure this team can improve very much because we have changed many players. Four years ago we almost achieved qualification and then we went to the European Championships,"
"But, I wait for the decision - I want to stay but maybe they're ready for another manager. I will continue with 100% commitment."
With their prospects of securing a place in Brazil and manager's job hanging by a thread, the Boys in Green knew nothing less than three points would be enough but failed to create any meaningful opportunities before Alaba pounced on Marc Wilson's loose clearance to clinch all three points for the hosts.
However, Trapattoni feels his players deserved at least a point from the game and was pleased with the individual performances of James McCarthy and Paul Green in particular.
"Our minimum aim was the victory and I thought we played well in the first half but we lost a bit of strength then. Robbie [Keane] had two good chances and it could have finished 0-0. Third position would have been fine for us so it's a pity." The Italian explained.
"Keane played well, and Long also but with this team, we have a limit. Austria were 51 per cent superior, we were 49%." He concluded.
The result leaves Ireland in fourth place in Group C, three points behind Austria and six behind second-placed Sweden.