Fournier's men missed their chance to move five points clear of Paris Saint-Germain atop Ligue 1, conceding two second-half goals in a loss to Lille.
Corentin Tolisso had given Lyon a third-minute lead before Lille struck twice in five minutes through Idrissa Gueye and Marcos Lopes in the second half.
The loss ended Lyon's 11-game unbeaten league run, and Fournier was seething afterwards.
"Our great run ends and I hope we will be capable of going on another one," he was quoted as saying by the Ligue 1 website.
"I am angry and legitimately so because every time we have the chance to open up a gap on the teams below us we don't take it. I hope we don't live to regret it in the coming weeks.
"I am very disappointed at the way the whole team played in the second half. Certain players' attitudes disappointed me."
If PSG win at Monaco on Sunday, Lyon will slip to second and be a point behind Laurent Blanc's men.
Fournier described the loss to Lille as a "huge blow"
"We can have regrets, especially after a quality first half, although we should have showed more ambition rather than just defending our lead," he said.
"After 40 minutes they changed their system but it was our lethargy in the second half that was the main reason for this defeat. It is a big blow.
"Their first chance weakened us and then they killed us with two goals in four minutes. We didn't have the resources to come back from that."
Lille coach Rene Girard lauded his team, who climbed into eighth and six points clear of the relegation zone.
"Our second half was remarkable. Hats off to the players. We knew we could do it but we still had to go out there and do it," he said.
"I am very proud of the boys. It is an important victory. We are not safe yet. We still need a few points."
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