JIM Boyce, FIFA’s outgoing vice-president, wants an investigation to be launched about the €5m payment given to the FAI.
"How anyone can authorise a payment of €5m to stop legal proceedings is totally and utterly beyond me," Boyce said about the deal which stopped the FAI from pursuing the matter.
"If this was authorised by the president of Fifa without the knowledge of the executive committee - this is something that has to be looked into. I sincerely hope that when they meet they launch a full investigation into it.
"It's just incredible and I can't believe that it's actually happened ... I've never known in my experience of football of someone giving a payment like that for a referee's mistake to stop someone taking legal action."
FAI chief executive John Delaney is adamant that the money received for the construction of the Aviva Stadium was ‘very legitimate’.
"It's a very good agreement for the FAI, a very legitimate agreement for the FAI.
"We felt we had a legal case against FIFA because of how the World Cup hadn't worked out for us with the Henry handball. Also the way Blatter behaved if you remember on stage when he had a snigger and a laugh at us.
"That day when I went into him and told him how I felt about him, there were some expletives used, we came to an agreement."
The sum was written off following the Republic of Ireland’s failure to qualify for the 2014 World Cup in Brazil.
On Thursday evening an FAI statement said: "The Association accepted Fifa's settlement offer to avoid a long, costly and protracted legal case. The offer given to the Association was fully written off by Fifa in 2014.
"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."