The former Italy and Juventus manager has retained the backing of the Chief Executive of the Football Association of Ireland, John Delaney, despite the home draw against Austria
According to Trapattoni, Delaney acknowledged that the team was 'unlucky' to concede to David Alaba in the last minute and that Ireland could still qualify for the 2014 World Cup in Brazil.
"[John Delaney] was in the players' lounge and [gave] me and (assistant coach) Marco [Tardelli] regards," Trapattoni told the Irish Examiner.
"For the result, obviously, (he) was no happy-happy, but for the commitment and for our performance, he said it was okay, we have played only 45 minutes now.
"He said we have again the other opportunity. I believe this, it's no problem. He said also, 'You were very unlucky'," he said.
"And not only him," continued the Italian tactician. "Also three or four people, not FAI, said, 'unfortunately you were a little bit unlucky this evening'."
After five games, Ireland are eight points behind Germany in Group C and level on eight points with Sweden and Austria. Sweden have a game in hand, but the 74-year-old remains optimistic about his team's chances of qualification and sought to take the positives from the last-minute home draw against Austria.
"This team in the future can learn from this," he said. "With more calm, we could have wasted a little bit of time with the free-kick and finished the game off. Instead, we played immediately and lost the ball in midfield."
He added: "Let me say one name: Damien Duff. In this position, he would go down, lose time and finish the game. That is experience."
He continued: "It's like arm-wrestling. Germany are out in front but Sweden, Austria and Ireland remain in this balance. And Sweden play Austria next.
"Can we still qualify? We have only played 45 minutes. Now starts the second round so why not."