The Italian tactician believes that the opening game in Group C against Croatia is extremely crucial to his side's chances of reaching the knockout stages
"We ourselves also know perfectly well that the first match is very important," Trapattoni told Uefa.com. "As important as the other first match, Italy against Spain. So the first 90 minutes will have an impact on the tournament."
He continued: "It's very important to win the first match, which would give us a certain advantage, but it would also be important not to lose. Then you'd need to judge it in light of the Italy-Spain result."
Turning his attention to the standard of Slaven Bilic's Croatia team, Trapattoni stressed that while they were probably more adventurous than the Boys in Green, there was little between the sides.
He said: "I have seen Croatia many times, and we have played them in a friendly as well, and I have to say, they have more creative players than we do. However, we are in the same physical and mental condition [as them].
"And with our tactics we have shown against Brazil and France how through our efforts, more creative players have failed to cause us problems."
The 73-year-old also believes that four points may just be enough to see Ireland qualify from the group, but stressed that his team always wants to win, regardless of the opposition. Drawing comparisons the Chelsea's Champions League victory, Trapattoni suggested that surprises were possible.
"If it's two draws, then it might be possible to qualify with four points," he said. "We want to win, to play and to score goals. But our opponents are strong. I think of the final of the Champions League, [what] Chelsea did against Bayern.
"Bayern had a lot more possession, they deserved to win, but lost of course and Chelsea created the best opportunity. Seventeen corners for Bayern, one corner for Chelsea – that is football."
And ultimately the Italian believes that his Ireland squad is mentally equipped to pull off a surprise at the tournament.
"That is one of our strong points," said Trapattoni. "Because we are strong in our attitude, our mentality, our confidence.
"Without a doubt we believe in ourselves. For us, this discipline, this attitude, is very important," concluded the Ireland boss.
Trapattoni's Boys in Green take on Group C rivals Croatia on Sunday June 10.