The 72-year-old Italian delighted with side's performance in tournament and believes victory can only spur them on in crucial Euro 2012 qualifier against Macedonia on Saturday
The Irish beat Scotland 1-0 on Sunday evening to finish top of the tournament table with a maximum of nine points from their three games, having comfortably seen off Wales and Northern Ireland in their previous matches.
Trapattoni was pleased with the way his players fought for the victory, and believes that with an important Euro 2012 qualifier against Macedonia coming up on Saturday, the winning mentality and quality his side have shown over the course of the tournament means the sky is the limit for what they can achieve.
"I said it would not be an easy game but we wanted to win this trophy," the 72-year-old told reporters.
"We are very satisfied. We tried three or four options and these options played very well.
"We scored nine goals and conceded nil. That is a demonstration that the team played with good discipline.
"I was confident about the result and when we play with this discipline and mentality it is possible to achieve every result.
"We can go to Macedonia with more confidence to achieve an important result."
The experienced duo of Shay Given and Robbie Keane both overcame frustrating club campaigns to play key roles in the Scotland victory, with Keane netting the winner and his 49th international goal.
Trapattoni cannot understand why some of his players have not been afforded first-team opportunities for their clubs, but the Italian insists it is the Premier League's loss.
"It is not my habit to cry about the English club's situation but this was proof our players can play in any English club," he added.
"I cannot understand why Robbie Keane, Shay or John O'Shea [do not play] but I am not the manager of the clubs.
"They play well with the national team and we win also."