Sunday's match was called off with 20 minutes to go after two pitch invasions and fighting between fans and police, BBC Sport reported.
Players on the visiting bench were attacked by Panathinaikos fans in the first pitch invasion after just four minutes at the Athens Olympic Stadium.
Olympiakos had been leading 1-0 and was awarded the victory.
"Panathinaikos FC condemns unequivocally every act of violence that took place at the Olympic Stadium and led to the permanent interruption of the derby," the club said.
It accused "a small minority of the 25,000 fans" of failing to respect football and added, "From the administration's point of view, absolute condemnation of all forms of athletic violence is essential."
It called on the Greek government to "finally show that it stands in the face of these events and find an effective way to definitively fight the violence in the stadiums".
Olympiakos midfielder Kostas Fortounis said it was "difficult" to play in the game and pointed out that Panathinaikos players had attempted to calm their fans down.
"Both we and Panathinaikos wanted to continue but when you enter the changing rooms twice and you go back, it's too hard," he added.
"It's tragic, I cannot explain it. Getting into the stadium, chasing the players... I have no words."
The first trouble broke out minutes into the game, forcing an eight-minute stoppage.
More violence followed after Olympiakos went ahead through Miguel Angel Guerrero in the 53rd minute.
Riot police attempted to contain the disorder with tear gas but as the gas started to affect the players, referee Marco Fritz called the game off.
Panathinaikos is expected to be punished with a points deduction and fine.