The Wigan midfielder was granted permission to leave the Irish squad after Sunday's 4-0 defeat of Georgia, ahead of Friday's World Cup qualifier against the Faroe Islands in Dublin, as he is suspended for the next competitive fixture.
However, Trapattoni is determined to take his strongest available playing party to the United States for the glamour tie against the world and European champions on June 11.
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."