The Boys in Green coach has stressed the positives after watching his side go down 1-0 to Greece at the Aviva Stadium
The Boys in Green enjoyed large spells of possession against Fernando Santos' men but failed to turn their dominance into a result as they went down to a single-goal defeat. However, Trapattoni opted not to dwell upon the defeat and stressed that several of his players showed their credentials.
"I think everyone who has seen the game and our performance will understand why the result was such a great disappointment to us," Trapattoni told reporters.
He added: "I watched the players show their personality in what was a very difficult team, they reacted well even after we conceded the goal and that is not easy."
"[Seamus] Coleman was fantastic. For me he was the man of the match. He must have delivered 20 crosses from the line. That is fantastic."
The Italian tactician also suggested that Ireland had been unlucky during the game, having had a number of penalty shouts turned down.
"And we were unlucky," he said. "After one minute the referee missed an obvious penalty. In the second half there is also one against Doyle. It’s not an excuse but these should have been penalties.
"That is football, though, there are the mistakes of the players, the mistakes of the managers and the mistakes of the referees. We have to accept them all."
Trapattoni praised the strength of the opposition, pointing out that they had performed well at Euro 2012 during the summer.
He said: "[Greece] is strong. It has played together a long time and they beat Russia in the summer. They are good but we did well against them.
"It was important to produce another good performance after the disappointment of Germany. I am happy that we did that. Again we saw the progression that was there against Kazakhstan and the Faroes," added Trapattoni.