Football Federation Australia (FFA) in response noted they had an obligation to act on Griffiths' abuse of a linesman, even if it wasn't picked up by its "routine procedures".
The Sky Blues had until midday on Monday to lodge an appeal with FFA after Griffiths was handed the ban on Friday for his misdeed in Sydney's 3-1 loss to Melbourne Victory at AAMI Park, six days earlier.
The suspension was a savage blow for Sydney on the eve of of their 2-2 draw to Newcastle on Saturday.
New recruit Griffiths will now also miss Sunday's clash with Brisbane and next week's encounter with Adelaide as the Sky Blues attempt to make a late charge for the finals.
While Sydney aren't contesting the ban they do have issues with Griffiths being charged retrospectively.
Normally a match commissioner and a referee's assessor attend each game while a member of the Match Review Panel (MRP) watches every game live on television.
Their notes, plus the referee's report, are collated and the MRP decide whether there were offences that need punishment.
No mention was made of the incident in any report review by the MRP with the Sky Blues left stunned when they cited Griffiths almost a week after the match and three days after it had met to discuss incidents from all matches that weekend.
"Sydney FC will not be appealing the decision to suspend Joel Griffiths for three matches and we are disappointed in what happened," chief executive Tony Pignata said in a statement.
"We have also asked FFA for clarification on the timing of the notification and subsequent suspension as we believe the process in this instance was inconsistent with previous MRP cases and raises concerns for all A-League clubs and players."
Sydney FC were only informed of the suspension at 5pm on Friday, after the team had departed for Newcastle with Griffiths forefront in coach Frank Farina's plans for the Jets match.
"We support the process as it is outlined to all clubs before the start of the season but it seems that process was not followed," Pignata continued.
"Who else is involved in the process? Can the MRP now be asked to adjudicate on issues retrospective of the event that clouds its independence?
"There are a lot of questions that I think all clubs and players would like answered."
FFA responded on Monday with A-League boss Damien de Bohun noting it was right for Griffiths to be banned, even though the MRP initially missed the incident.
"We were dealing with an incident that was initially missed by the routine procedures and that affected the normal timelines," he said in a statement.
"To be clear, the incident was reported to FFA by several sources later in the week. In this case the incident warranted referral to the MRP.
"It doesn't matter how the incident is reported. If the laws of the game and the A-League Disciplinary Regulations are breached and the incident falls within the jurisdiction of the MRP, we have an obligation to act.
"We were dealing with a red card offence, corroborated by video evidence and the admission of a player."