Williams has received a lengthy ban for his part in the incident
Harlequins chief Mark Evans has written to the club's fans to apologise for Tom Williams feigning a blood injury against Leinster in April.
The winger was banned for 12 months after being found guilty of faking an injury in the Heineken Cup semi-final.
"We have to accept we have been found guilty of behaviour that cannot be accepted or condoned," Evans wrote in an open letter on the club's website.
"And for that we apologise to all of you unconditionally."
Williams' appeal against the severity of his ban will be heard by an independent panel in Glasgow on Monday.
Director of rugby Dean Richards was cleared of wrongdoing by European Rugby Cup's independent disciplinary committee, but he resigned from the club at the weekend.
It was no surprise to me or the board that [Dean Richards] wanted to take full responsibility for events
Chief executive Mark Evans
Evans paid tribute to Richards in his letter on Wednesday, but admitted the former England star had "taken full responsibility" for what had happened.
"I would like to thank Dean on behalf of the club for his enormous contribution over the last four seasons," Evans added.
"His input has been absolutely central to the improvements the club has made on the field and I am sure that I speak on behalf of the players, staff, board and supporters in thanking Dean and wishing him all the best in his future.
"It was no surprise to me or the board that he wanted to take full responsibility for events. One mistake, albeit extremely high profile, should not overshadow a career in which so much has been achieved."
Evans said the club was now focussed on trying to reduce the length of Williams' ban and to prevent the club being excluded from European competition.
ERC disciplinary officer, Roger O'Connor has appeal against the leniency shown to Quins by the independent disciplinary committee that banned Williams.
The club was given a 250,000 euros (£215,000) fine, with 50% suspended for two years, while the complaints against Richards, physio Steph Brennan and doctor Wendy Chapman were all dismissed.
Evans added that "we must not let one event negate years of hard work that have been put in over the last decade to get us into the position we are in today".
The club has initiated its own "independent inquiry" into what happened when Williams was replaced by fly-half Nick Evans with five minutes remaining of the Heineken Cup quarter-final against Leinster.
Television cameras spotted Williams winking towards the bench with "blood" smeared around his mouth.
Harlequins managed to engineer a late drop-goal attempt for Evans but the New Zealander was struggling with a knee injury and pulled it wide.
Evans is currently deciding how best to replace Richards
The club's chief executive said the internal inquiry had "already resulted in a number of outcomes".
"Aside from Dean's resignation, we have written to Leinster to formally apologise unreservedly for the incident," said Evans.
"We have appointed an independent person to continue the internal review looking at every aspect of this affair but his remit is wider - allowing him to examine any other similar behaviour and helping us to ensure we put stronger processes and policies in place.
"We must now work to ensure that the highest of standards are upheld. I am confident every professional rugby club across the country, and indeed further afield, will be looking at this incident and will learn from how we deal with it.
"Our organisation needs better processes and procedures. We have been naive in this regard, but I assure you that we have learnt from this and will endeavour to uphold the great name of the club and rugby as a whole."
Evans said the club was currently looking at how best to replace Richards. It could appoint a direct replacement for the former Leicester director of rugby, or restructure the coaching staff.
In the mean time, the existing coaching team of John Kingston, Colin Osborne and Tony Diprose "will temporarily take on some of the responsibilities left by Dean's departure including team selection and dealing with the media".
"The board will ensure that issues such as players' contracts and strategic decision making are not overlooked," Evans added.