FA chairman Greg Clarke, chief executive Martin Glenn, technical director Dan Ashworth and human resources director Rachel Brace were questioned by British MPs on the digital, culture, media and sport committee for two hours on Wednesday.
The session started with the publication of a reopened investigation into Chelsea player Eni Aluko's claims against Sampson of bullying and discrimination.
Unlike a previous internal FA review and an earlier inquiry by barrister Katharine Newton, the third probe found that Sampson had made racist remarks to Aluko in 2014 and teammate Drew Spence in 2015.
From what checks were made on Sampson before he became England women's manager, to why the FA was withholding half of an 80,000-euro settlement from Aluko, the MPs savaged the way the English game's ruling body treated the bullying, racism and sex allegations that contributed to Sampson's dismissal last month.
Having started his evidence to the committee with an apology to Aluko and Spence over the racist remarks, Glenn refused to accept the FA's entire response was flawed, while Clarke would not apologise personally to Aluko.
Glenn denied trying to coerce Aluko into making a statement that the governing body is not institutionally racist.
The 30-year-old striker had earlier told the panel she has not received a second tranche of the settlement she agreed with the FA earlier this year so as to avoid going to an employment tribunal following her allegations against Sampson.
Aluko, who has 102 caps for England, said she was told by Glenn that she would get the rest of her money, which was to compensate her for loss of future earnings, if she wrote a statement clearing the FA of racism.
She said she categorically refused to write it, considering it to be a request that bordered on blackmail.
Glenn refuted Aluko's claim, saying the FA had stopped the second payment, due after this summer's European Championship, because of a tweet Aluko sent on 30 August.
That Twitter message said: "At least we now know the FA's stance on derogatory racial remarks by an England manager. Ignore, deny, endorse. In that order."
Glenn said the FA took legal advice and decided it breached their agreement not to defame each other.
When asked if the FA officials should consider their positions following the hearing, panel chairman Damian Collins said: "Yes, I think they have to look very carefully at the evidence given today.
"I think it was disappointing that not even until right at the end was Greg Clarke prepared to admit the FA should apologise for failings in its process - quite serious failings in a process the individuals on that panel were responsible for."
He added: "The question should be: Does what you've seen today inspire confidence and do they understand the issues well enough to put in place the right systems to ensure it doesn't happen again? And I'm not convinced."