The side saw their chances of qualifying for the World Cup in Brazil recede as a result of a damaging 2-1 defeat at the hands of Sweden on Friday
Goals from Johan Elmander and Anders Svensson ensured that Robbie Keane's opener did not affect the outcome of the 2014 World Cup qualifier.
Speaking after the defeat, Trapattoni was reluctant to blame his players and still retained the mindset that qualification for next summer's finals in Brazil is a possibility.
"We started very well and took advantage in the first half," the Italian told RTE. "But two episodes decided the match. They played physically. They took the two opportunities very well. They scored. They took these two opportunities. In the first half we had more shots.
"At the moment, we are third. We need to win in Austria. We need a result in Germany and after we must beat Kazakhstan.
"Against Georgia we showed this personality and we have to have more conviction. We can't give Austria the same opportunities. We have to think about our mentality, our attitude."
Republic of Ireland take on Austria in Vienna on September 10.