The Thursday evening fixture in France saw the game delayed by 45 minutes as people spilled on to the pitch after fighting broke out between the rival fans and missiles were thrown.
There was also violence outside the Parc Olympique Lyonnais stadium before the game, which Lyon won 2-1 with a late winner.
“The first priority of the home team is to provide a game played in secure and healthy conditions,” Besiktas spokesman Metin Albayrak told Anadolu Agency.
“Everything… is under the responsibility of Lyon. There is no need to punish Besiktas.”
UEFA is expected to open an investigation into the events and is likely to launch disciplinary proceedings against both clubs.
However, Albayrak insisted: “If there is one who would be punished, it is Lyon, not Besiktas.”
According to a statement from the local municipality, seven fans and five police were injured in scuffles before the match. Twelve supporters from both clubs were arrested.
Albayrak said Besikas had notified UEFA before the game that tickets were being sold illicitly.
“If a twentieth of the incidents were carried out in Turkey, Turkish clubs would be heavily punished,” Albayrak added. “Such incidents do not happen in Turkey... I am proud of my fans.”
Photographs on social media showed black-clad Lyon hooligans, who have a history of violence and neo-Nazi sympathies, attacking a group of Turkish fans that included women and children.
During last year’s European Championships, Lyon supporters attacked English fans ahead of an England-Slovakia fixture and three years earlier the club was nearly expelled from Ligue 1 following a brawl with Marseille fans.
In September 2015, they displayed a banner reading “Refugees Not Welcome” at a home match against Lille.
Albayrak said the French fans would be welcomed with Turkish hospitality at the return match on April 20 in Istanbul.