More than 20 ex-footballers have now come forward with allegations after former Crewe player Andy Woodward waived his right to anonymity to speak publically about the abuse he suffered as a child by convicted paedophile Barry Bennell.
Five separate police forces, including Greater Manchester Police and the Metropolitan, have subsequently launched investigations into the claims while the FA has opened its own review.
When asked if offences could have been swept under the carpet, Clarke said: "I don't know if there was a cover-up or not, I really don't know.
"I suspect like many big problems, people aren't drawn towards them. My methodology is, if there's a problem, run towards it, embrace it, fix it, disclose everything that happened.
"I think institutionally, all organisations in the old days used to protect themselves by keeping quiet and closing ranks. That's completely inappropriate and unacceptable today.
"It's certainly the biggest (crisis) I can remember. I think the moral consequences of failing to deal with some of these issues in the past we must get to the bottom of."
Despite Clarke’s words, the FA has come under fire for its handling of the scandal.
Damian Collins MP, chair of the Commons Culture, Media and Sport Committee, has accused the FA of being slow in responding to the growing allegations.
"I think we've acted very quickly, to be frank,” Clarke said in response to such criticism.
"The main thing to do is not to encumber the criminal investigations of the police by tainting their evidence.
"We've agreed with the police that we won't talk to any of the victims formally, because they have to talk to them, they have to take statements and we're not allowed to interfere in that process."
A number of former Crewe youth team players have now gone public with their own stories after Woodward first spoke out earlier this month.
Steve Walters, Chris Unsworth and Jason Dunford all later told BBC’s Victoria Derbyshire programme that they had also been abused by Bennell.
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