Trapattoni's side were thrashed 6-1 by Germany last night, raising questions over the veteran manager's future with the country.
However, the 73-year-old has refused to consider quitting, and is confident that his players are in full support of his management.
Asked what would make him consider his future, he replied: "When there is no positivity, when I ask the team to do something and they do not do it.
"I said to the team, 'Right, what can we do? You can tell me if you don't believe this or this or this, why?'. I have never said to the team not to stay back and not to try to score goals. We give them jobs and we have a system to get goals, and the players believe in this.
"The team tries to do what we ask and they are happy to do it also."
Ireland's next match comes away to the Faroe Islands on Tuesday.