After Wednesday night's 1-1 draw with England, Ireland now take on Georgia, then face the Faroe Islands in a World Cup qualifier before finally encountering world and European champions Spain in New York on June 11.
The latter fixture will not be easy given the Irish are at the end of an arduous season, whilst Spain are preparing for their Confederations Cup campaign. Trapattoni said: "England are one of the strongest three, four or five countries in the world. I look at my group, and three or four are young. They need experience."
He added: "Only against a great team and great players can they grow. There's only one football. You have to keep confident and keep trust in each other, because we play with the same lungs as our opponents.
"Against England I asked them to show we can play without fear. Only with this can we grow. I am really happy from what I saw, from James McCarthy and Seamus Coleman. Shane Long was clearly the best on the pitch.
"I know what this result meant because I saw they were a bit tense in the dressing room and the next friendly game against Spain will be another great opportunity."
Trapattoni reserved particular words of praise for goalkeeper David Forde. The 33-year-old Millwall keeper has been installed as Trapattoni's new first-choice keeper, replacing veteran Shay Given whose exclusion at Aston Villa has cost him his international berth.
Forde was excellent, making key saves from Alex Oxlade-Chamberlain and Theo Walcott on the rare occasions when the Irish defence was breached.
"He saved some good shots," said Trapattoni. "But more important than that, he showed us good personality. That is our aim.
"After Given, it was important to see a performance like this. Forde gives us confidence. Also he gives our defenders confidence."
- Sports & Recreation