Benrahma was set to join the Ligue 1 club on Thursday, but an 'admin error' meant the paperwork was not completed by the deadline.
The 28-year-old is believed to have even been pictured in a Lyon tracksuit before the deal collapsed, with a £15million fee having been agreed.
After the deadline passed and the paperwork was not completed, the French club launched a scathing attack on West Ham.
A statement read: "Olympique Lyonnais strongly regret the failure of the transfer of Said Benrahma, for reasons beyond our control, and question the behaviour of West Ham, who failed to finalise the required administrative procedures despite all the agreements concluded.
"Olympique Lyonnais were delighted to welcome Said Benrahma to Lyon this Thursday to finalise his transfer from West Ham.
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"The two clubs had signed a temporary transfer agreement, and Olympique Lyonnais had obtained the approval of the DNCG to allow the transfer to take place in a fluid and transparent manner.
"However, in the early evening, when Olympique Lyonnais had entered all the administrative data on FIFA's dedicated platform (FIFA TMS), West Ham had never launched any technical procedure on their part, despite OL's repeated reminders and continuous mutual telephone communication.
"In the absence of this reciprocal action on the part of the English club and following this incomprehensible behaviour, raising questions, the international transfer certificate could not be requested before closing time.
"Olympique Lyonnais deeply regret this situation and this decision, demonstrating a deep lack of respect on the part of West Ham for the Institution and the player.
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"The club reserves the right to initiate all appropriate procedures necessary to validate the operation later, and to hold West Ham accountable if necessary."
Fulham also tried to hijack the deal on deadline day, while there were also offers from Turkish clubs.
There will also be concerns about whether Pablo Fornals will complete his move to Real Betis with no confirmation that the deal has gone through with all the necessary documentation at the time of writing.