The club presidents of Lyon and Marseille faced the media on Sunday evening after the teams' Ligue 1 match was abandoned.
Marseille midfielder Dimitri Payet was hit in the head by a bottle of water thrown from the stands on while taking a corner kick.
Payet collapsed to the ground in the fifth minute of the fixture at Lyon but was able to get up after receiving treatment. The referee ordered the players to head back to the locker room as play was suspended.
After the game was called off, Lyon president Jean-Michel Aulas told a press conference that the home side had "all the security measures to prevent any major incident with 56-thousand fans in the stadium."
"We have 350 security cameras in the stadium that allow us to identify every troublemaker - and this is what happened today. Whereas in the past, it was not the case. Sometimes the organizer doesn't want to go and get the troublemaker. Here, obviously, it has been done clearly. We must take some decisions but we don't have to punish the club who did everything well."
Opposite number Pablo Longoria commented: "These are situations we must all think together about, with all the French football decision-makers, because it goes beyond the limits of a lot of security measures."
It is not the first time this season that a French league game has been marred by a violent incident.
A match between Nice and Marseille in August was abandoned after fans threw projectiles and invaded the field. Payet was also hit by a bottle in that game and threw it back at the fans. Players and staff members were also involved in a brawl.