The force also revealed that, so far, 15 people had been arrested or reported to prosecutors over violent scenes which marred the aftermath of the game.
Rangers said its players and backroom staff were assaulted when fans invaded the pitch at Hampden Park.
Hibernian won the game 3-2 - the club's first cup win since 1902.
Det Supt Kenny Graham, who is leading the investigation, said, "Our focus at the moment is on reviewing video and images in order that we identify those who were responsible for causing disorder, violence and anti-social behaviour on the pitch, not those who may have been caught up in the crowd.
"I am sure that there are people who witnessed or have captured incidents on their mobiles and it's vital that we speak to them so we can view any material that could help us.
"Similarly, I am keen to appeal to the media to send any footage or images to us, as well as members of the public, as this could assist with the inquiry."
The detective urged fans and members of the media who had images or video of the disorder to send them to: ScottishCupFinalPitchInvasion@Scotland.pnn.police.uk
He said a "dedicated inquiry team" had been set up at Govan Police Office "to investigate acts of criminality".
Det Supt Graham said officers were currently reviewing CCTV footage and other video and photographic images to identify those involved.
The final ended in chaos when thousands of Hibernian fans flooded onto the pitch as they claimed their first Scottish Cup success in 114 years.
Amid the celebrations some Hibs supporters are alleged to have attacked Rangers players and backroom staff as they attempted to leave the field.
Some Rangers fans also made it past stewards and on to the pitch, leading to a period of fighting between the two sets of supporters before mounted police and stewards restored order.
The pitch invasion delayed the presentation of the trophy and there was no lap of honour for Hibs players.
Rangers players were not able to pick up their cup final medals.
The SFA has since announced that an independent investigation will be held into the scenes of disorder.
Police have launched a dedicated email address to receive images and video which captured scenes of disorder after Saturday's Scottish Cup final.