Ireland finished bottom of Group B having been defeated by Croatia, Italy and the world and European champions Spain. However, the 73-year-old is determined to carry on in his role as coach, despite suggestions that he should step aside.
"A philosopher has said that when a man has no interest, he is dead," the Italian told reporters.
"I have a well of energy and enthusiasm far bigger than the oil wells of Libya, Saudi Arabia and countries like that.
"I desire to live, to learn, to train, to come up against the rest of the world. And I want to get revenge for Ireland after these Euros."
Trapattoni admitted mistakes had been made during the summer, but also believes his team can come back stronger.
"I have made some mistakes and I do not sleep at night thinking about them.
"The team can be rejuvenated. There are some interesting talents, starting with Darron Gibson.
"There is him and James McCarthy, someone we couldn't bring here because there was an unfortunate family illness.
"There are some veterans like Robbie Keane and Damien Duff that we need to talk to, to figure out if they want to continue."
The coach believes that the occasion may have been too much for his side, but denied that the campaign was a disaster.
"I remain proud of this group. We weren't right from the start against Croatia, when we seemed overcome with tension and emotion.
"Spain were too strong for us, but against Italy the true spirit of Ireland re-emerged.
"We were missing a lot, especially on corners and free kicks. We have to be more careful but the team has found itself and its credibility again.
"This is what we must repeat because the tournament has not been a complete disaster — it will serve as a great experience for us.
"The European Championship is difficult with a match every four days, but it will serve us well for the World Cup [qualifying] campaign."
Trapattoni admitted he would also experiment with his side in upcoming fixtures, and admitted that Irish football was not at the same level as other countries.
"We will experiment, even if time is short. The friendly against Serbia on August 15 will tell us something.
"You have to admit that Irish football is not yet at the level of others.
"There is too big a difference between league and international football.
"The team still has a long way to go. Maybe we lack a bit, but we have good basic technical skills and our performance against Italy will increase our confidence.
"Nothing is impossible. I believe in my players."