Hibernian and Rangers both saw Scottish Football Association disciplinary charges dismissed by an independent judicial panel on Wednesday.
The panel dismissed as "irrelevant" charges over damage to advertising equipment and, in the case of Hibs, the Hampden pitch and goalposts following a mass pitch invasion by both sets of fans.
The SFA failed to punish either club because its disciplinary procedures are not underlined by "strict liability" - where clubs are responsible for their supporters' behaviour
A Scottish Government spokesperson said: "The disorder that marred the Scottish Cup final was unacceptable and we are disappointed by this outcome
"It is essential that robust, meaningful measures are in place to allow such behaviour to be dealt with effectively
"Independent research shows that fans overwhelmingly support the goal of eradicating offensive behaviour from matches.
"We have been clear that we will take steps if the progress we need to see isn't being made
Our preference remains that football should proactively deliver a solution and we are continuing to work closely with the authorities and clubs to encourage them to do so."
SFA members voted against the adoption of strict liability in 2013 while the Scottish Professional Football League also does not take action if clubs successfully argue they have taken all reasonable steps to prevent unacceptable behaviour among fans.
Any direct interference in the SFA's workings would not be popular with FIFA - the world governing body has issued bans to nations whose governments have become too closely involved with football federations.
Hibs welcomed the panel's decision on Wednesday and paid for damage caused when their fans invaded the pitch
Rangers have made no comment since the SFA announcement.
More than 70 people have been arrested over the violent scenes which took place after Hibernian's late 3-2 victory earned their first Scottish Cup win since 1902.
Source : PA
Source: PA