Ireland's hopes of qualifying for the World Cup in Brazil next year took a major blow when they were beaten 2-1 by Sweden on Friday, giving the Swedes the edge in a three-horse race for second place in Group C.
However, Trapattoni believes that his five-year stint in charge of Ireland has been a success even if his side do not reach next summer's World Cup, highlighting their controversial exit at the hands of France in a playoff for the last World Cup and their qualification for Euro 2012.
"I continue my job. After this, if I was [Football Association of Ireland chief executive] John Delaney, I would say, 'Giovanni, continue because Giovanni has done a great job in these five years'," Trapattoni told reporters. "First was [the World Cup playoff in] France - and you know what happened. We changed again and we achieved [qualification for] the Euros, and we changed again.
"In the Euros, we played against Spain and Italy, who finished first and second. When I assess what we have done until now, we have to continue to do it. I promised change and promised to discover new players, young players, and the players have changed.
"I would like to have this new team at a club because I would have the possibility to work every day, every week with this team. I am sure I could develop this team, their quality and their experience very much."
Ireland currently sit fourth in Group C but could move back level on points with Sweden if they beat third-placed Austria tomorrow night.