Lyon president Jean-Michel Aulas has said his side's exit from the Champions League is "a huge disappointment for us and for French football."
Last season's Ligue 1 runners-up conceded in injury time as they lost 2-1 at home to Belgian champions Gent on Tuesday.
That result means Lyon do not have the consolation of a place in the Europa League -- which a third-placed finish would have given them - and are guaranteed to finish bottom of Group H.
Lyon are second in Ligue 1, but Aulas said the lack of quality they showed and the injuries they had suffered made them uncompetitive in Europe.
"It's better, at that point, to be knocked out and to concentrate on the league," he told reporters.
"But that doesn't take away from the disappointment, which is huge for us but also huge for French football because we weren't able to pick up points.
"And it's true that, after that, the whole of French football is penalised as a result of our below-par performances in the Champions League."
Lyon have taken only one point from five group matches, which has hit France's position in the UEFA rankings that determine the number of European places allocated each season.
France were sixth before the season but are now on course to be overtaken by Russia, which could result in the loss of a Champions League place in future.
"The disappointment is big," Lyon boss Hubert Fournier said. "We can't say too much when we have one point from five matches. The record speaks for itself.
"We didn't meet the standard required. During this competition, there wasn't one game during which we raised our level. There were bits of games, a half, but never a full match."
Gent, however, have a good chance of qualifying for the last 16 on their debut in the competition.
The Belgians are a point ahead of Valencia in second place, meaning a home win over already-qualified group winners Zenit St Petersburg would see them qualify for the knockout stages.
"We took more than we deserved," Gent manager Hein Vanhaezebrouck said of the Lyon game.
"That doesn't happen very often, but it doesn't make it any less enjoyable."