Damien Duff, who wore the skipper's armband in Monday's 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.
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, 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 - (we) 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."