In the wake of Ireland's tournament-ending 4-0 defeat to Spain on Thursday - their second Euro 2012 defeat in two games - Keane was highly critical of those involved in Gdansk and was annoyed by the way the players were serenaded from the stands despite their heavy loss.
The 40-year-old wrote in his column in the Sun: "You'll never beat the Irish? It's time for that song to be put away because, at the moment, everyone is beating them. I'm sick of this 'win, lose, we're on the booze' mentality. It has to change."
Keane notoriously walked out of Ireland's 2002 World Cup campaign, meaning some fans have refused to give his comments any credence.
But the former Manchester United midfielder is ready to stand by his comments, especially if challenged by players he believes do not deserve their place in the side.
"The likes of (Robbie) Keane, Shay Given, Richard Dunne, John O'Shea and Damien Duff are picked every game as they have a big reputation. A reputation for what? They hadn't qualified for anything in 10 years," he said.
"They love having a dig back when I say something but I tell you now, I'll be ready if they do because players have to be accountable for how the team did.
"I'm trying to be constructive but the manager and players all have to be accountable. It's not good shrugging our shoulders and having a sing-song."
Keane did seek to clarify his comments about the supporters, though, adding: "People seem to have misunderstood me. I've no problems with the fans singing. It's great that they back the team during and before games - but should they really stay on long after the final whistle cheering?
"There's a danger that the players think that what has happened on the pitch is acceptable, when it's not."