A year on from their last meeting, Ireland and Spain will face each other in an international friendly fixture due to take place in Yankee Stadium, New York
The two sides last met at the European Championships in Poland, where the competition's eventual winners Spain triumphed by a score of 4-0. Nevertheless, the former Italy and Juventus boss hailed the "confidence" and "balance" of his team and believes that they can give a good account of themselves.
"There is confidence in our system and balance," Trapattoni told reporters. "I don't know if we can win, but we won't be humiliated."
Of the team that lost to Spain in June 2012, only four remain in the squad for Tuesday's clash in New York. Sean St Ledger, Simon Cox, James McClean and Robbie Keane are the only survivors from that game, indicating a much-changed Ireland squad.
And Trapattoni feels that his team has the opportunity to continue their "growth" by building upon their recent performances against England, Georgia and the Faroe Islands.
"In the last three games, the players have shown us they are well," said the Italian tactician. "We are conscious of our quality."
He continued: "We got a good result against England and while England are not like Spain, because Spain is more creative and technical, I think we can do well."
Meanwhile, Trapattoni has urged Wigan Athletic midfielder James McCarthy to "believe in himself" and to "become famous" by playing well against Spain.
The Ireland boss suggested that McCarthy, along with a number of other Irish players, had an opportunity to display their credentials to other clubs when they take on the world and European champions.
"I said to James that you have the opportunity to play against this great side, the fantastic Spanish players, and this can be your chance to become famous," he told reporters.
He added: "I think that some of our players can play for the great teams, and this is a chance to show that."
"He must believe in himself because he has good quality, good vision, and shooting also, but he should be more enterprising."
The Republic of Ireland take on Spain on Tuesday, June 11 at Yankee Stadium, New York.