Keeper Shay Given, 36, and 31-year-old skipper Robbie Keane, the nation's two most-capped players, in particular were unable to reproduce their best form in Poland and Ukraine as Ireland slipped out of the competition having failed to claim a single point.
But Trapattoni said: "When you do your job well - until now, I think they have played well for our country, and we must have a reason.
"In your job, when you get old, if they gave you a pension and say. 'Go' without respect, what would you think?
"It's not loyalty only, it's correct. We asked them yesterday for a good performance and we played very well. We played at the same level as Italy.
"We need a reason to change it on the pitch. [Aiden] McGeady played well, [Kevin] Doyle played well, also Robbie.
"It's not loyalty, it's respect because they helped us to achieve qualification and we must give them the honour of playing.
"You are not sure that if you make changes, the result will be any different. It's 50-50. When you are sure, you can change, but only after the 90 minutes can you be sure that the change is good.
"Until now is has been good, and I can't just turn the page and forget about it. It's not professional, it is not correct."
The Republic's involvement in the competition came to an end last night with a 2-0 defeat by Italy in Poznan, although their hopes of reaching the qualification were already long gone.
Rumours have been circulating for several days that some of Trapattoni's senior men, including Given, Keane, Richard Dunne and Damien Duff, could announce their retirement from the international game in the wake of the tournament.
None has yet done so formally, but the 73-year-old, who revealed last night he had spoken too "one or two" players about their futures, is hoping they will stay on to help blood a new generation.
He said: "I can say the names, but I won't say the names. I am sure they need to stay with their families, I don't know.
"But I said two months ago, it is important for us that these senior players help also the young to gain new experience. That's life, it is not only football.
"The young are usually arrogant or shy and the senior players help them grow. That is life, it is not only football."
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