After Nice full-back Lloyd Palun was shown a second yellow card in the 54th minute for conceding a penalty, Lyon captain Maxime Gonalons equalised from the spot for the home side, only for the visitors to claim victory thanks to Valentin Eysseric's spot-kick with four minutes remaining.
The loss saw Lyon give up top spot in Ligue 1 as they remained one point behind Paris Saint-Germain and Fournier was frustrated by his side's lack of experience as they dominated possession following Palun's expulsion.
"The team are disappointed with the performance and the result, especially the last half hour in which we lacked collective maturity," Lyon's coach said.
"Instead of moving the ball around, being patient and finding a way around the Nice defence, we rushed things. Our finishing was not good enough but we can't be too critical of an attack with an average age of 21 and a team without the experience of handling a match like this."
In the lead-up to the weekend's Ligue 1 action, Fournier had insisted his team were not title favourites, despite topping the French top flight for 10 straight weeks.
With the likes of veteran defender Henri Bedimo, star striker Alexandre Lacazette and up-and-coming full-back Samuel Umtiti - who were all suspended - Fournier claimed he had been worried about Lyon's chances against Nice.
The south coast club ended a four-game losing streak at the Stade de Gerland, while it was Nice's first victory in eight Ligue 1 fixtures.
"We knew this was the game where we could get caught out because Nice are fighting for their survival and we were missing key players, and that showed at times," Fournier said.
"This will allow us to gain the experience and maturity that we were lacking tonight. We don't have the same squad as Marseille, Paris or Monaco, but so far we have done well."
