Olivia Pinkney, Sussex Police deputy chief constable, said the officers, who are new in service, were working on the cordon some distance from the scene.
She said the video did not show details of the site but a message attached to it was inappropriate and offensive.
She said families of the victims were disappointed to learn of the incident.
Eleven people died when a vintage Hawker Hunter jet crashed on to the A27 during the Shoreham Airshow on 22 August.
Ms Pinkney said the force had apologised to the relatives and had admitted the families had been caused unnecessary distress.
The footage and message were sent on social media to a colleague who reported the pair, she said.
"Those officers have let themselves down, of course, but most importantly they have let down the 11 families of the local men who died that day," Ms Pinkney said.
The police chief said she had thought about suspending the young constables, who are still in their probationary period, but she said she wanted them to "keep their shoulder to the wheel".
The officers, based in Brighton, have been assigned duties away from the public.
Ms Pinkney said the allegation impacted on everyone affected by the crash and detracted from the professionalism of hundreds of colleagues.
She also said she was disappointed and upset by having to investigate two colleagues over the incident.
Two police officers being investigated for gross misconduct after the Shoreham air crash filmed themselves near the scene, it has been revealed.