Speaking for the first time since Foley admitted he felt "betrayed" by the 73-year-old after he had lost his place in the final 23 to Paul McShane, Trapattoni was in feisty mood after training at Borgo A Buggiano.
The Italian, who was clearly agitated by repeated questions on the matter, said: "I have already explained to you why I chose between two players with different characteristics. I don't have anything else to add.
"We speak about the training. We speak about what we can do again. The team is happy and playing well.
"I don't wish to speak again about this situation. Finished. Finished. Finished."
But asked specifically about Foley's use of the word "betrayed", Trapattoni added: "I was betrayed also.
"But I ask you: is Paul McShane an Irish player or a foreign player? I called in another Irish player, so I don't see the problem.
"I also clarified why. For the position, for the position. The position is for defender, it is clear. I didn't call a striker or a winger. I am finished with this question."
Foley, who was initially named in the 23-man squad, reported for duty with a hamstring injury and spent the first week or so in Dublin working his way back to fitness.
He trained at the Stadio Comunale Alberto Benedetti on Monday ahead of Tuesday's friendly against a Tuscan Select XI the following evening.
But he was devastated to learn on the morning of the game that, fearing injury or suspension could decimate his pool of central defenders, Trapattoni had decided the more versatile McShane, who had earlier been called into the travelling party from the stand-by list, was the better option for the final list submitted to UEFA.
The veteran Italian invited the Wolves full-back to remain with the squad, but after playing the second half of the friendly in neighbouring Pistoia, he slipped away from the team hotel in Montecatini yesterday morning and headed home.
There has since been speculation that he is unlikely to play for Ireland again as long as the current manager remains in post, although Trapattoni was non-committal.
He said: "He knows my opinion. We will let him stay quiet and think about what he will do. It's no problem. He must decide what he wants to do."
Asked if he has realised how angry Foley was, he replied: "No. He said he was disappointed."
The saga has sparked a debate over whether or not Trapattoni should have named such a small squad - 23 players plus another five on stand-by - as early as May 7, rather than calling up more players and then whittling it down.
Italian counterpart, Cesare Prandelli, has done just that, but the Ireland manager is adamant he will have faced exactly the same problem.
The former Italy boss said: "You have to think that 50km from here, there is another national team. They have 32 players. Think about the nine players that will go home.
"It [the situation] is gone. We have a responsibility to the team and with the country. We are professional, we are not idiots, not idiots.
"It is the same. To decide one or two or four is the same. They would all be disappointed.
"I have already explained to you in Italy many years ago that seven went home and seven were disappointed."
If Trapattoni was prickly, he was at least able to comfort himself by the return of keeper Shay Given and John O'Shea to full training today.
Given had rested since jarring his knee in Malahide on Monday last week, and O'Shea had joined up with an ankle injury.
Both played a full part in the session and clearly enjoyed being back amongst their colleagues.
Trapattoni indicated that both would play in Monday's friendly in Hungary, and that the bulk of those who start that game will also line up against Croatia in their opening Group C game on June 10.
Asked how the two key men were, he said: "Perfect. Shay Given I think is no problem. We will start the team in the last test that probably also 90 per cent will start the Euros."