Trapattoni and his players are due to fly out to the United States at the weekend after Friday night's World Cup qualifier against the Faroe Islands to finish their campaign with a friendly against Spain.
There will be absentees - Stoke defender Marc Wilson is scheduled to undergo surgery to remove a metal plate from his leg, while West Brom striker Shane Long is to be married - but otherwise, the Italian is expecting a strong turn-out.
That may have come as a surprise to Wigan midfielder James McCarthy, who was allowed to leave the squad after Sunday's friendly victory over Georgia as he is suspended on Friday evening.
McCarthy is also nursing a groin problem but, if it has anything to do with Trapattoni, he will be on the plane.
The 74-year-old said: "It's important. I have a family too but it's professional discipline. You can make other time to rest.
"When I was a player, I never turned down these opportunities. Players need to rest as they have played many games, but it's also important to see on the list the famous names like [Richard] Dunne, [John] O'Shea and McCarthy.
"We have accepted to play this game against Spain and the Irish people in New York deserve respect. They are paying for tickets, but not to see the second team.
"Our players must understand that it's only for three days."