The Europa Conference League game on Thursday, which ended in a 1-1 draw, kicked off almost an hour late after crowd trouble erupted in the stands and left one person in critical care.
TV footage showed Cologne supporters making their way towards the home fans and throwing flares. Local authorities said 32 people were injured.
"Our sports minister summed it up: We're sick of it! When you witness that first-hand, it's terrible," Rivere told a news conference on Friday.
"And the day after, being able to take a step back, seeing the images, it's even worse ... That's not what football is about. It's intolerable.
"I'm not the sort to jump ship when things aren't going well, but when you're in the middle of that, of course, you ask yourself, 'What am I doing here?'"
Paris St Germain said on Friday they were contemplating legal action after some of their supporters were involved in the incident in Nice.
European soccer's governing body UEFA has opened disciplinary proceedings against the two clubs.
"Will there be punishments because the incidents happened inside the stadium? Do you want to punish the city too because they caused a lot of damage there?" Rivere added.
"We suffered events and of course, we have made a complaint to police."
