Social Democrats TD Catherine Murphy has called on the FAI to "play ball" and get its house in order.
She said the refusal of former chief executive John Delaney to answer questions about FAI finances at yesterday's Oireachtas Committee hearing was "about as frustrating as it could have been."
Speaking on RTÉ's Morning Ireland, she said Mr Delaney has been "Mr FAI" for a very long time and was the most person best placed to answer the Committee's questions.
Ms Murphy added that while it was true that Mr Delaney did not have to come before the committee yesterday, she would have hoped that an organisation in receipt of sizable State funding would have used the opportunity to try to rebuild some confidence and trust.
This was not, she said, Mr Delaney's attitude.
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She said just a few FAI board members knew about the €100,000 loan given to the association by Mr Delaney, and that the treasurer only found out about the loan just before a report on it was published in the media, which said a lot about how the organisation was run.
Ms Murphy called for changes in the FAI, saying it was not possible to have confidence in the organisation following yesterday's committee meeting.
She said the FAI received streams of funding from government, including sports capital grants and large scale capital grants.
An Assistant Professor at the School of Law and Government at DCU said the "primary legal reason" that Mr Delaney declined to answer questions yesterday was because he was attending on a voluntary basis.
Dr Tom Hickey said this voluntary attendance meant that Mr Delaney was not compelled to answer any questions and he could have left at any time.
Mr Delaney cited the Angela Kerins judgment as underpinning legal advice that precluded him from answering a number of questions.
Dr Hickey said this was "convenient legal advice".
Speaking on the same programme, he said that while the Kerins judgment "hovered menacingly over yesterday's proceedings", the two episodes were very different.
He pointed out that there had been "a severe breech of fair procedures" in the Kerins case when she was asked a number of questions that she had not been given advance notice of, which was not the case yesterday.
