The defeat equalled Ireland's worst loss at home and led to calls from former players, commentators and local media for the ex-Italy boss to be fired.
However, after Tuesday's 4-1 victory away to the Faroe Islands gave Ireland two Group C wins out of three, the Football Association of Ireland said qualification for the 2014 finals in Brazil remained a realistic and achievable prospect.
"The board, while disappointed like everyone with the poor result and performance against Germany and understanding the frustration of some of our supporters, reaffirmed that Giovanni Trapattoni is to remain in charge of the national team," the FAI said in a statement.
"The board recognises the depth of feeling surrounding the team, the performances, the results and the manager, reflecting the passion which everyone in Irish football has for the game and will continue to work closely with the manager."
Ireland's next qualifiers are away to second-placed Sweden and at home to fourth-placed Austria.