The governing body of football in Europe, Uefa, said it was investigating the role of both clubs during the events at the stadium.
It said charges against CSKA Sofia include damage to the stadium, throwing objects, racist and/or discriminatory behaviour, crowd disturbances and violating decent behaviour.
Charges against Derry City include effective invasion of the field of play, throwing objects, crowd disturbances and insufficient protection of the playing area against intruders.
In a statement, Derry City Football Club said it “unequivocally condemns the violence witnessed at tonight’s match”.
“The club is working closely with UEFA, the PSNI, CSKA Sofia and our security partners to establish the full facts surrounding the incidents,” it added.
A spokesperson for CSKA Sofia said the club plans to present Uefa with information relating to “the organization – or lack thereof – concerning security, the conditions, and the overall staging of the football match in Derry by the host club and the Northern Irish authorities”.
The club added they condemn “all acts of aggression, inappropriate behaviour, and hooliganism”.
The BBC has asked Derry City FC and the PSNI for further comment.