Ireland's Euro 2012 adventure ended with another defeat on Monday night as Italy beat them 2-0 in Poznan to leave them with no points in three games.
Trapattoni has declared his intention to continue into next season's World Cup qualifying campaign but the team's performance in Poland and Ukraine has raised question marks as to whether, at 73, he is the right man to lead them forward.
Asked about the prospect of Trapattoni being forced out, captain Keane simply said: "No chance."
Los Angeles Galaxy striker Keane may have left little room for doubt about Trapattoni's future but the same could not be said about his own.
Indeed, none of Ireland's veterans were making snap decisions about their international careers after last night's game.
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 on Monday 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.
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 disappointed."
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 this 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 yesterday, said: "It's very hard because we've been preparing for this and dreaming. You don't want to be thinking about the finish.
"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."
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