He told Sky News this was the most serious problem he could remember to have hit English football.
Clarke was referring to the serial child molester Barry Bennell, who has been accused by at least 20 footballers of abusing them when he worked for Crewe Alexandra, Manchester City and Stoke City across three decades beginning in the 1970s. He is subject to five separate police investigations.
The FA has also launched its own internal review, appointing leading lawyer Kate Gallafent, an expert in child protection, to head it up.
The FA said the review would find out "what information the FA was aware of at the relevant times around the issues that have been raised in the press, what clubs were aware of, and what action was or should have been taken".
Clarke took over as chairman in August and has already had to deal with the departure of Sam Allardyce as England coach over comments he made in a newspaper sting and a row with FIFA over the wearing of poppies.
But he told Sky News this was the most serious problem he could remember to have hit English football.
"It's certainly the biggest (crisis) I can remember," said Clarke.
"I think the moral consequences of failing to deal with some of these issues in the past we must get to the bottom of."
Clarke does not know if the FA at the time deliberately turned a blind eye to the goings-on, although a reporter who made a documentary about sex abuse in football for Channel Four in 1997 has claimed there is an FA report from 2005 detailing 250 victims and spread over a number of clubs.
"I don't know if there was a cover-up or not, I really don't know," said Clarke.
"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."
Clarke told the BBC that the FA review would not seek to speak to alleged victims, nor would he confer with his predecessors as chairman.
"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," said Clarke, who added he thought criticism of the present FA was misplaced and they had acted speedily to look into the claims.
Bennell, who has served three jail terms for previous abuse, is presently hospitalised after police responded to a "fear for welfare incident" but it has not halted the string of victims coming forwards.
Another appeared on Tuesday as former Wales Under-18 international captain Matthew Monaghan told the Daily Mail for the first time of the abuse he suffered at the hands of Bennell when he was a boy at Crewe.