The president of the Hillsborough Family Support Group has told ESPN the FA should never have chosen the ground for the 1989 FA Cup semi-final and called for a full internal inquiry into why it was selected.
Trevor Hicks said: "They need to face up to what they did and to be accountable for what they did."
Sheffield Wednesday's ground did not have a safety certificate and had been the scene of previous dangerous crowding incidents, but FA officials picked it to host Liverpool versus Nottingham Forest for a second successive year.
Ninety-six Liverpool fans lost their lives in a crush at the Leppings Lane end in Britain's worst sporting disaster. For the second time in a row, Liverpool fans had been allocated that stand - smaller and with far fewer turnstiles than Hillsborough's Kop - despite having the bigger support.
A report by the Hillsborough Independent Panel, published on Wednesday, cleared Liverpool supporters of any blame and exposed a devastating cover-up by the police and emergency services, aided and abetted by some media coverage.
On Thursday, 23 years after the disaster, English football's governing body issued an apology through its chairman, David Bernstein. He said: "We are deeply sorry this tragedy occurred at a stadium the FA selected."
But Hicks said that did not go far enough and called for a full internal FA inquiry into the choice of Hillsborough. He also urged the association to play a full role in any further Hillsborough inquiries sparked by this week's report.
Hicks, who lost two daughters in the disaster, told ESPN: "The FA took us to a ground that was dangerous. It had been pronounced unsafe - but it was worse, it was dangerous.
"It is clear that the FA did not check it out properly. But it was the FA's choice. There were problems in 1988 as well, another crushing incident - although that happened outside the ground. There was a catalogue of errors, far worse than what the Taylor Report said about it.
"We have had an apology from the FA, but they need to go further. They need to face up to what they did and to be accountable for what they did."
Hicks acknowledged that the FA had made all the relevant documents available to the independent panel, but stressed: "It's now time for everything to be re-examined by the agencies of the state that have let us down all these years. The Prime Minister has apologised and pledged that the state will now do what it needs to do."
Adrian Bevington, the FA's communications director, said the FA was "deeply regretful" about what had happened and shared the sadness of those who had lost friends and loved ones at a football match that was part of its own competition.
In an interview with Sky, Bevington said the FA had said sorry because "the suitability of the venue had been questioned". He said the association would wish to play a full part if any new inquiry questioned its role.
The Taylor Report highlighted that dangerous situations had arisen at Hillsborough in the years before 1989.
In 1981, Tottenham played Wolves in an FA Cup semi-final at which Tottenham fans were hurt in crushing at the Leppings Lane end. On that occasion, people were directed into emptier areas of the terracing in time to stop the situation from worsening.
In 1988, when Liverpool had also played Forest, there was severe congestion and crushing outside the Leppings Lane turnstiles - a situation that arose again in the minutes before the 1989 disaster.
Lord Justice Taylor wrote: "In selecting Hillsborough as the venue for the cup semi-final, the Football Association did not consider in any depth whether it was suitable for a high-risk match with an attendance of 54,000 requiring to be segregated, all of whom were, in effect, away supporters lacking week in, week out knowledge of the ground.
"No special inspection was made; no consultation with Sheffield Wednesday or the local authority took place.
"I have little doubt that, if the disaster scenario had been described to the management at Hillsborough prior to 15 April 1989, they would have said: 'Of course, it couldn't happen here.' Yet something like it had happened at Hillsborough in 1981, albeit with less dire results."
Sir Alex Ferguson has echoed his Liverpool counterpart Brendan Rodgers in calling for an end to the tasteless chants about Hillsborough and the Munich air crash that have been heard from some supporters at games between Liverpool and Manchester United.
He said: "You would hope that maybe this is a line in the sand in terms of how the supporters behave with one another. The fact we are playing them after the findings we have been reading about in the last couple of days does bring a focus to it.
"Both clubs have suffered fatalities through football. You hope that fans do behave themselves and support their team and that will be the end of it.''
Meanwhile, the chief constable of West Yorkshire Police, Sir Norman Bettison, has apologised after releasing a statement on Thursday in which he said Liverpool fans had made the police's job harder.
Bettison, a South Yorkshire chief inspector in 1989, is the most senior police officer who was involved with that force's operations in the aftermath of the disaster. West Yorkshire Police Authority, along with the South Yorkshire force, is to investigate the conduct of officers including Bettison.
Saying he had "nothing to hide", he had claimed: "Fans' behaviour, to the extent that it was relevant at all, made the job of the police, in the crush outside the Leppings Lane turnstiles, harder than it needed to be. But it didn't cause the disaster."
But in an updated statement released on Friday, he said: "Let me speak very clearly. The fans of Liverpool Football Club were in no way to blame for the disaster that unfolded at Hillsborough on 15 April 1989.
"I can be no plainer than that and I am sorry if my earlier statement, intended to convey the same message, has caused any further upset."
He said his role "was never to besmirch the fans", adding: "There wasn't a black ops unit and I wasn't a part of it, I was a part of the team that was trying to put together the facts."
One of the hundreds of thousands of documents examined by the report panel revealed that in the days after the disaster, Bettison – who had attended the match as an off-duty spectator - claimed "aggressive" Liverpool fans had attacked police cars during the rescue operation. He alleged that many had been without tickets.