A joke by FIFA president Sepp Blatter about Ireland's failure to qualify for the 2010 World Cup sparked the "extraordinary" €5m payout to the FAI, the association claims.
The association last night answered a growing clamour for transparency on the deal with a detailed statement.
It reveals the negotiations behind the €5m payoff to Irish football following Thierry Henry's infamous handball in a crucial World Cup qualifier - and that the decision to allow the subsequent goal to stand had only been one of the factors for what followed.
In the aftermath of the November 2009 game, FAI officials met with FIFA "to raise the hurt caused to the Irish people by what had happened, the damage done to football in Ireland and worldwide".
The FAI said it was agreed the meeting would remain confidential, but days later Blatter made a joke of Ireland's bid to be the World Cup's 33rd team.
This was "in breach of confidentiality" and "brought reputational damage to the FAI" which led to the €5m payout being agreed at a meeting in Zurich.
FAI chief executive John Delaney said: "I've heard a lot of talk over the last couple of days about selling the fans down.
"I'm an Irish fan, I love my country, I love the Irish national team. I was doing my best with members of the FAI board to get us back with a sporting solution."
The FAI at first looked for a "sporting solution" to the issue - a replay or an extra place at World Cup 201 - before seeking compensation.
Mr Delaney revealed that the legal claims by the FAI were based on FIFA's decision - in the weeks before the playoff games in late 2009 - to seed the draw. This, the FAI CEO claimed, was essentially a rule change, and one of the factors that gave Ireland a potentially strong legal case. However, there is no mention of the seedings in the documents released by the FAI last night.
Mr Delaney further outlined how Mr Blatter's comments to the media in late November 2009 had been a catalyst for the financial deal.
"He spoke on November 30 about our confidential meeting on November 27, and he made a skit ... he knew and we knew that it was of damage to the FAI."
Asked about whether the money was hard to see within FAI accounts, Mr Delaney said there was full disclosure and also cited a confidentiality agreement.
He told RTÉ that documents were being placed on the FAI website to show how the money arrived, and was spent on the Aviva Stadium.
He said: "There was a fine (in the confidentiality agreement) of a quarter of a million dollars if we spoke about, or disclosed the fact that we had got this money from FIFA."
However, he said that the money was present on the books, and was contained within the turnover figures of 2011 and 2013.
"I think it's unfortunate that this story has got caught up with all the other stories about FIFA. This was a good, legitimate business deal for the FAI."
The FAI revealed that after negotiation, FIFA offered the €5m interest free loan by way of compensation, as well as a $400,000 Goal Project grant that was used for FAI Regional Football Centres.
It said the loan was used to make payments to New Stadium Ltd (the trading name for the Aviva Stadium management company) on February 25 and March 26 of 2010, totalling €6,772,711.25. The loan was subsequently written down meaning the FAI did not have to repay it.
The revelations capped a day of growing pressure for transparency on how the deal was done.
Earlier, former FAI chief executive Bernard O'Byrne had urged: "If the explanation is clear and simple, get it out as quickly as possible.
"If it's a simple story then everyone can have the truth and they can make up their mind whether the decision taken was fair or good or the opposite."
Former chief executive of the FAI Fran Rooney had also said that the deal puts the FAI in a "bad light" and called on them to publish the details of the settlement.
"Confidential payments of this nature are at odds with transparency. This confidential agreement should not have been confidential and should have been disclosed at the time," he said.
Former Ireland midfielder Keith Andrews said he believes that the FAI lost their dignity by accepting the €5m.
The 34-year-old, a star performer for Ireland on the night Henry's handball ended their World Cup dream, told Newstalk that "disbelief and disgust" were his primary emotions when he learned of the arrangement.
"As a country, we were able to hold our heads high with great dignity, that was the one comfort we all had, and now that's been taken away from us. That's very sad," said Andrews.
"There was a lack of transparency. It wasn't a loan. It was hush money to get rid of John Delaney, the FAI and anyone saying anything about negative about FIFA."
However, in its initial statement on Thursday, the FAI insisted the deal was legitimate.
"FIFA's settlement with the Association has at no time influenced the FAI's criticism of FIFA as demonstrated by our consistent criticisms of Sepp Blatter. Furthermore, the settlement was made without any conditions other than confidentiality."
Why would anyone get too exercised about the precise amount of money which came out of FIFA's slush fund to buy the silence of the FAI? Five million dollars, 3.6 million pounds, or 30 pieces of silver? What's the difference?
Our two nations have made up off the field. Did we ever think we would see the day? The dismemberment of the stadium formerly known as Lansdowne Road by English football hooligans needs to be replaced at the front of the cue of memories by a more orderly, sporting and peaceful occasion.