The 73-year-old Ireland coach, author of phrases such as "don't say cat until you've got it in the bag", told a news conference, among other things, that "the robe does not make the monk".
"There is a lot of jealousy, a lot of envy," he added at one stage, without mentioning who he was referring to or why.
"Some people become uneasy when other people get good results."
Having also spoken of "philosophers and generals", he recalled the words of Umberto Agnelli who was president of Juventus when Trapattoni coached the Turin side.
"He told me that to understand young people, it was important never to say that it was better in my day," he said.
"In Italy, we have a simple phrase: 'the ball is round.' With a little bit of fantasy, and sometimes a small mistake, it makes us believe in little things."
He added: "If you want to keep improving, you must never lose your curiosity."
Asked about the prospect of Ireland meeting his native Italy in a potentially decisive final group game, Trapattoni moved on to his eating habits.
"I think about what I'm going to eat tonight, not what I'll eat in three days," he said.
Trapattoni, who has won domestic titles in Italy, Germany, Austria and Portugal and played at the 1962 World Cup, also warned of how the best-laid plans could go astray.
"It's like the eve of the final match of the championship. Everyone is expecting victory and I'm thinking about mistakes that could lead to non-victory. That's my only, but great, worry," he said.
"I prepare everything down to the last detail, but one unforeseen moment, or slip-up, could lose the match. It gives us a sensation of impotence, but we still have conviction."
Trapattoni's captain Robbie Keane, sitting alongside the coach, was more down-to-earth.
"We're not here to make up the numbers, there's certainly a lot of confidence in the squad," he said as Ireland entered their first major tournament since the 2002 World Cup.
"There's no doubt that these players are going to this competition believing they can get out of this group.
"The country has been on its knees for a few years and this has certainly given the country a lift."
