Crewe have been criticised for issuing an apology to victims of serial abuser Barry Bennell which is "cold, mealy-mouthed" and "almost begrudging".
The Offside Trust, a charity set up by survivors of sexual abuse in sport, has also called for former Crewe manager and director of football Dario Gradi to be stripped of his MBE.
On Wednesday, an independent review of historical sexual abuse found the Football Association was guilty of inexcusable "institutional failings" in delaying the implementation of child safeguarding measures following high-profile convictions.
The review by Clive Sheldon QC was commissioned by the FA in December 2016, shortly after former player Andy Woodward spoke out about having been abused at Crewe by youth coach Bennell.
Bennell had been convicted in the United States during 1995 of sexually abusing a 13-year-old British boy on a tour.
In February 2018, Bennell was sentenced to 31 years in prison for 50 counts of child abuse against 12 boys aged eight to 15 between 1979 and 1991. Judge Clement Goldstone QC described Bennell as "the devil incarnate". He was sentenced to a further four years last year.
Crewe were one of eight clubs whose conduct was investigated as part of the Sheldon review, but only issued a formal response late on Thursday afternoon, in which the club apologised for not doing more to act on any warning signs to stop Bennell.
The Offside Trust responded in a strongly-worded post on Twitter, which read: "Crewe's belated statement is welcomed 'if' it is indeed sincere.
"We are pleased to see the club finally say 'sorry', shame it has been delivered in such cold, mealy-mouthed, legalistic fashion.
"The emphasis on their lack of culpability makes it sound almost begrudging.
"The Sheldon Report recommends that safeguarding training is undertaken by club directors.
"The FA might want to do the first one of these at Gresty Road."
The Sheldon review concluded Gradi "should have done more" to investigate or escalate reports and rumours of abuse by Eddie Heath during his time at Chelsea and later Bennell at Crewe.
However, the report said Gradi himself had not acted inappropriately in any of his interactions with boys, either when they stayed at his home or in any other setting.
The Sheldon review detailed the fact that, at a 2003 civil case, Bennell claimed that Gradi and other senior figures at Crewe knew he was a paedophile.
It also references the fact that Gradi "did not consider a person putting their hands down another's trousers to be an assault" when Sheldon had a general discussion with Gradi about abuse. When Sheldon told him that it was assault, Gradi accepted.
The FA confirmed on Wednesday that Gradi had been suspended since 2016, with chief executive Mark Bullingham saying he "did not see that changing".
Gradi had told The Times on Wednesday that he was unaware he had been suspended.
The Offside Trust called for Gradi to be stripped of his honour, which was awarded in 1998 for services to football.
"We're writing to Cabinet Office to request forfeiture of the MBE," the Offside Trust said in a statement on Twitter.
"We will be making similar requests to the PFA and Football Hall of Fame to revoke other honours. Symbolism matters."
In the wake of the Sheldon review's publication, FA chief Bullingham offered a "heartfelt apology" to the survivors of historical sexual abuse.
Crewe's statement issued on Thursday read: "The club acknowledges the findings of Mr Sheldon QC that, notwithstanding the club may still not have got to the truth of any matters at that time, more could have been done to monitor the situation concerning Mr Bennell.
"The club is truly sorry if there were in fact any warning signs that ought to have led the club to do more.
"Had the club had any suspicion or belief that Mr Bennell was committing acts of abuse, either before, during or after he left the club's employment, the club would have informed the police immediately."
Crewe's statement continued: "The club wishes to make it absolutely clear that it sincerely regrets and is disgusted by the terrible crimes committed by Mr Bennell upon many young footballers over a significant number of years.
"The despicable abuse committed by Mr Bennell was abhorrent and the club continues to have the deepest sympathy for the victims and survivors of Mr Bennell.
"The club fully understands the additional hurt and trauma to the victims and survivors of Mr Bennell which has been caused by the fact that no one at the club was aware of the offences being committed upon them at the time.
"The club wholeheartedly regrets and is sorry to every survivor of abuse that it was unaware of Bennell's offending."
The FA "fully supported and accepted" the findings of the Sheldon review, with the governing body adding that steps were already under way to implement those recommendations as part of a "wider safeguarding strategy".
Crewe also expressed regrets over historical failings in the club's own safeguarding policy.
"The report of Clive Sheldon rightly acknowledges that for most of the period of Mr Bennell's and others' offending there was little or no guidance on child protection available to those working in sport or society in general," the Crewe statement added.
"The club acknowledges that awareness of child protection matters and systems of safeguarding in football and in society have now improved considerably and safeguarding has become an integral part of the club's everyday life.
"The club acknowledges however that improvements to safeguarding can always be made and the club accepts the recommendations made by Clive Sheldon QC to ensure our safeguarding procedures remain as robust as possible.
"The club also acknowledges the contributions made by all individuals to the report of Clive Sheldon QC and reiterates its deepest sympathy to all those victims and survivors of Mr Bennell."