Quinn revealed that he had been under the impression that Keane would issue an apology on Irish television on Monday for his abusive tirade at McCarthy.
But when Keane did not do so, the 22 remaining players voted unanimously against their former captain's inclusion back into the squad.
There were not any players throwing their arms up in the air saying 'yes bring him back'
"If Roy Keane had apologised on television I am sure he would have been on his way to Japan," said Quinn, who was close to tears during the news conference.
"We came so close to getting Roy out here. He will never know how close.
"The vote was unanimous. It was 22 players, during a a very hard five to 10 minutes, but there was no lobbying.
"Every single player was asked for their opinion and we came out of that meeting with the first statement we issued.
"We had no alternative, but it did not rest easy with Mick.
"There were not any players throwing their arms up in the air saying 'yes bring him back'.
"The lads are a bit shattered, there's no doubt about that.
"But the structure of the Irish team had to come before Roy and with a heavy heart we issued our statement.
"There is also frustration in our camp, but hopefully today that will start to go away.
"We're trying to draw a line under all of this."
Quinn added that he had tried to act as an intermediary to negotiate Keane's return by contacting the player's solicitor Michael Kennedy.
"The word coming back from various sources was that a plane had been booked and that Keane was going to apologise on television," said Quinn, who admitted he had not slept all night waiting for the interview.
"I tried to call Michael Kennedy just after our meeting, but it was the middle of the night.
"I think Michael knows that there's probably not much point of a phone call now.
"The conversations I was having with Michael were that Roy was coming around all the time and that the TV was going to be the big one.
"I didn't want to see Roy lose out and I wanted to try to salvage winners on all sides if possible.
"The people back in Ireland changed the players' minds.
"But we have spirit and heart in the camp and we are united,
"All 22 players are fully committed to Mick."