Keane, who won seven Premier League titles during a 12-year stint at United under Sir Alex Ferguson, was unhappy about the training facilities in Saipan.
In May 2002, having threatened to exit the team once, he told the Irish Times that the pitches were “rock hard”.
“I can’t imagine any other countries in the world who are far worse off than us, playing on something like that,” Keane said.
He said he was not being a “prima donna” and called the facilities “dangerous”.
Days later, during a team meeting, McCarthy demanded an apology from his captain in front of the squad.
“I think Mick’s intention was to drop it on Roy in public,” Kiely said.
“I don’t know whether he wanted to embarrass him.”
Either way, the famously combative midfielder responded to McCarthy’s interrogation with a lengthy tirade. Legend has it that Keane told McCarthy “I didn’t rate you as a player, I don’t rate you as a manager and I don’t rate you as a person.”
Kiely said the silence following his departure felt like “an eternity”.
The then Charlton keeper said he tried to break the tension with a joke, saying: “I can play in the middle of the park if you need, Mick.”
In the absence of their best player, the Republic of Ireland, who shared a group with Germany, Saudi Arabia and Cameroon, reached the last 16 of the tournament, where they were narrowly beaten on penalties by Spain.
Keane would not resume international duty until after McCarthy had departed from his first spell in charge of the national side.
The Republic of Ireland have not reached a World Cup since.
Kiely said the side could have gone further in the competition had Keane not exited.
“We would have been much better set with him playing in the middle of the team,” he said.
