The Boys in Green grabbed a narrow win over Bosnia-Herzegovina on Saturday but Trapattoni insists he was more concerned with getting a win than putting on a show.
"Ten years ago [at the 2002 World Cup], the old Ireland side played very well but in the past 10, 12 years, it is completely different football," the Italian told reporters.
"What I ask always of the team is that we believe in ourselves. We have shown them what we want them to do and they understand.
|Ireland 1-0 Bosnia
"I have said many, many times, there is the show and the result. You can have a beautiful show, but without a good result.
"After three days, the result remains, but the show is forgotten, and they understand this."
The 73-year-old has faced criticism for supposed old-fashioned techniques but the former AC Milan, Inter and Juventus manager has firmly stated that he is as forward-thinking as any coach.
"I have had many opportunities in the past also because I played in finals as a player," Trapattoni continued.
"But that is the past. It is important I show everyone I am still useful.
"That's important because football changes and it's important I go with football. I still know about the old football.
"There are teams that win and there are teams like Bayern [Munich] which played better [than Chelsea] and lost the Champions League final. That's football.
"I follow this football, the new football, every four years, it changes. The referees change, the culture changes."