Around an hour before kick-off at Nice's Allianz Riviera ground on Sunday, some fans in the away end ripped out seats and began throwing them at supporters in the home section.
The situation required police intervention, upon which visiting Saint-Etienne fans were escorted from the stadium en masse. Nine people were injured during the incident, according to the French Ministry of Interior.
Through a statement on his club's website, accompanied by a picture showing the empty, damaged section of seating, Rivere said: "I am appalled. What I've seen is unacceptable.
"It can not happen in a stadium. There was never a problem at the Allianz Riviera (before).
"That's all we do not like to see in a football stadium, especially as we strive for the matches here (to be) a party to bring women (and) children.
"I do not subscribe to that. This is a problem. There are solutions to be taken."
LFP president Frederic Thiriez echoed Rivere's sentiments and went on to suggest that the league would look to ban travelling supporters in the event of any further disturbances.
A statement from Thiriez read: "Enough! The few cretins who claim to be supporters do not even realise they are ruining the image of football.
"I will ask (for) a meeting with the Ministry of Interior to discuss the supporters' trips to away games. If we don't solve this problem permanently it will end with a systematic ban on (supporters') trips, which nobody wants."
