"If certain strong sides are going home, this means that Italy have the quality to go right through to the end of the tournament," he told a news conference.
Trapattoni said Ireland had regained some pride with their performance after wilting in a 3-1 defeat by Croatia and 4-0 reverse to Spain.
"I think this evening we played much better than the games against Spain and Croatia. We played with more personality, credibility, commitment," the Italian surmised, adding that Italy coach Cesare Prandelli had said Ireland had troubled them.
Trapattoni, who also suffered the disappointment of an early exit as Italy coach at Euro 2004, said the first-half goal by Antonio Cassano effectively ended the game not the 90th-minute second from Mario Balotelli.
"The first 20 or 30 minutes we played well, we had our possibility to score, [but] after one goal the game was already finished," he said.
He also revealed that some unnamed Ireland players had approached him about plans to retire from international football, but that he would be advising them to wait a while before making a decision.
"Now is too early, [but] I can also say to you that I spoke just now with one or two. We'll see again in the next friendly game in August," Trapattoni said.
"Maybe in this moment they are disappointed. This is in the air, [so maybe it is better for them if] they wait to see what happens."
Whatever happens about the futures of players such as Robbie Keane, the 73-year-old said that despite the disappointment and criticism of his tactics and team selection, he intends to remain in the job for the World Cup 2014 qualifiers.
"[I have a] willingness to believe again, because I am sure we have fresh energy in this new squad and we can do better. I wait... to start again in the new season," he remarked.
