Crewe chairman John Bowler has resigned following the publication of the Sheldon report into historical sexual abuse in football.
The League One club apologised and said they acknowledge “more could have been done to monitor” Bennell.
In a statement, Bowler apologised again to the survivors and said he always intended to resign after the review.
“As the only person left with an association to that era, I truly believe it was important for me to see it through to conclusion,” he said.
Bennell is serving a 34-year jail term for abusing boys between 1979 and 1991 while at Crewe and Manchester City.
Bowler, 84, had been chairman since 1987, having first joined the board in 1980.
The Offside Trust, a group set up by survivors for survivors of childhood sexual abuse in sport, welcomed Bowler’s resignation but criticised the time taken to make the decision.
“We thought it might have been made in 2016. And again in 2018,” it said.
“For it not to have happened once the Sheldon report was published rubbed salt into the wounds of survivors.
“It has taken several days of pressure from survivors, journalists and ultimately the club’s own supporters to force this resignation today.”
Crewe previously said they were not aware of any sexual abuse by Bennell until 1994 when he was first convicted of sexual assault, and did not receive a single complaint about sexual abuse by him.
In his statement, Bowler continued: “I am satisfied with the findings of the review that found that the club did not have any knowledge of Barry Bennell’s heinous crimes.
“I will always be deeply appalled and sorry that those young players and their families suffered at the hands of this evil predator.
“I personally and sincerely apologise to them all for their suffering.
“Crewe Alexandra is a community-based club with good people. I apologise to all our supporters that the name of the club has been tarnished.”
What did Sheldon say about Crewe?
Sheldon said former Crewe manager Dario Gradi “should have done more” to investigate concerns about Bennell but was not involved in a cover up.
Last week Gradi apologised for “not recognising signs of abuse” carried out Bennell.
The report also said: “It is likely that three directors of Crewe Alexandra FC discussed concerns about Bennell which hinted at his sexual interest in children.
“There is no evidence that the advice of a senior police officer to the club’s former chairman to keep a ‘watching brief’ on Bennell was heeded.
“The club should also have ensured that there were appropriate arrangements in place for boys staying overnight at Bennell’s house.
“The boys should have been spoken to periodically to check that they were being properly cared for. Had such steps been taken, this might have led to boys making disclosures to the club.”
Crewe’s apology following the report’s publication was criticised by survivors and Crewe’s MP, Kieran Mullan, called for the club’s leadership to stand down.