After Serbia's Stefan Mitrovic pulled the flag down, a brawl broke out between both sets of players, as well as Serbian fans, some of whom invaded the pitch.
A statement released by the Albanian FA said: "Civilians entered the pitch causing a melee, punching Albania players and hitting them with stools. Furthermore, our players were also hit by stewards and security personnel serving at the game.
"Making their way to the dressing rooms, in the tunnel, Albania players were repeatedly hit by Serbia supporters, security personnel and the police.
"Also, before the Albanian players were allowed to leave the stadium, with orders from Belgrade prosecutor general, according to the police, the entire staff and players of the Albania national side were physically searched. Police went through each member's and player's personal belongings."
UEFA has opened disciplinary proceedings against the two nations following the incident.