The Wolves defender has spent the last week desperately trying to shake off a hamstring injury and trained with his team-mates at the Stadio Comunale Alberto Benedetti in Borgo A Buggiano yesterday afternoon.
However, his name was not among the 23 submitted to UEFA this lunchtime when the final squad was confirmed with 24th man Paul McShane getting the nod instead.
Trapattoni said: "With the injuries that we experienced in the squad over the past week, I have had to make a tough decision when it comes to naming the 23 players that must be submitted to UEFA for the championship.
"Kevin Foley, John O'Shea, Paul McShane, Darren O'Dea, Shay Given had all been carrying knocks and we have been monitoring them closely in their recovery.
"Although Kevin has been recovering well, I have made the difficult decision to leave him out of the 23-player list after completing fitness tests on John O'Shea and Paul McShane this morning.
"I have spoken to him and understand how difficult it is, saying that he can remain with the squad if he wishes."
Foley is the second man from the initial 23 to miss out following the departure of midfielder Keith Fahey at the weekend as Paul Green flew in to take his place ahead of the Republic's departure for their pre-tournament training camp in Montecatini, Italy.
However, Trapattoni was relieved to be able to include Given and O'Shea in particular with the 36-year-old goalkeeper expected to return to full training tomorrow after resting a knee injury and the 31-year-old defender, who has been battling an ankle problem, hoping to play some part in this evening's friendly against a Tuscan Select XI in Pistoia.
There could still be leeway for Trapattoni to make further changes should injury strike again, but that option is available to him only until the day of Ireland's first Group C game against Croatia on June 10, and even then only after convincing UEFA's own doctors.
Trapattoni has Tuesday night's game and then a final friendly against Hungary in Budapest on Monday to check on the fitness of his players, and he has told O'Shea in particular that he will have to prove to him that he is ready ahead of the big kick-off.
Ironically, McShane himself sat out training last night with a bruised heel, while fellow defender O'Dea rested a thigh problem, although in both cases, their absence was precautionary.
It proved an eventful morning for Trapattoni and his players, who attended a civic reception in Montecatini last night.
Tremors from the earthquake which struck 210 kilometres to the north were felt in the spa town, as was an after-shock around four hours later.
The FAI released a statement which read: "An earthquake was experienced in Parma, 210 km away from the Irish team's training camp in Montecatini this morning at 9.03am.
"Tremors were felt in Montecatini. Nothing was noticed on the ground floor of the team hotel. However, some light movement was experienced in the higher levels.
"Everything is fine in camp. The thoughts and prayers of Giovanni, (his assistant) Marco (Tardelli) and the squad at this time are with the dead and injured in the neighbouring Emilia Romagnan region."
The Ireland squad will spend the next four days in Tuscany before heading for Budapest and subsequently Poland, where they will finalise their preparations in Gdynia near Gdansk.
Ireland's squad for Euro 2012: Shay Given, Sean St Ledger, Stephen Ward, John O’Shea, Richard Dunne Glenn Whelan, Aiden McGeady, Keith Andrews, Kevin Doyle, Robbie Keane, Damien Duff, Stephen Kelly, Paul McShane, Jonathan Walters, Darron Gibson, Keiren Westwood, Stephen Hunt, Darren O’Dea. Shane Long, Simon Cox, Paul Green, James McClean, David Forde.