Captain Robbie Keane and Shay Given - the two most capped players in Ireland's history - and veteran defender Richard Dunne all insisted they would take time to consider whether they would play on.
Damien Duff, who wore the skipper's armband in the 2-0 defeat to Italy to mark his 100th cap, seemed to hint his time was up, having previously revealed he had made up his mind whether to play on or not.
Ireland's Euro 2012 misery was complete, with defeat seeing them finish rock bottom of Group C with zero points.
Los Angeles Galaxy striker Keane, who earned his 120th cap in Poznan, said of his future: "It's not probably the right time even to be talking about it.
"The whole squad has come off a tournament and we're all disapppointed."
Asked when the right time might be, Ireland's record goalscorer, 31, added: "I'm not even really thinking about it to be honest with you."
Goalkeeper Given, 36, who made a record 125th Ireland appearance on Monday evening, said: "It's too soon straight after the game to make any rash decisions.
"I'll sit down with my kids and my wife and my family when I get home and just see what the best plan of action is.
"Obviously, we've got a new manager in at Aston Villa - I'd like to speak to him as well - and see what the best plan is for everyone."
Winger Duff, 33, said: "I've said I'll play until 100 for Ireland if they'd have me.
"Sometimes, it doesn't work like that. So we'll see.
"It's more important to talk about the team and how we've done over the past month.
"Obviously disappointing - weren't good enough."
Dunne, 32, who made his 76th international appearance, said: "It's very hard because we've been preparing for this and dreaming. You don't want to be thinking about the finish.
"As soon as this comes around, you want to play and concentrate on this.
"Now probably is the time for whoever has thought about it to have a month away and make a decision in a month's time maybe.
"You've just been hammered three times and you're probably just sick of football at the moment.
"You just want to go away and think about it and start again in July and, as far as this is concerned, see what happens."
Keane may have been coy over his own future but asked if there was any prospect of manager Giovanni Trapattoni being forced out, he said: "No chance."