Fournier's men returned to the top of Ligue 1 with the point, leaping above Paris Saint-Germain thanks to their superior goal difference.
They managed to earn a point despite having Lindsay Rose sent off in the 29th minute at the Stade de Gerland.
"I am both proud of my players and disappointed," Fournier said.
"I am very proud of what we were able to produce in term of quality of play, the opportunities created and the fact of not giving up despite the adverse events that got us in trouble.
"This proves that we have the character but also the quality. We are disappointed with the result but not with the performance of the team."
Clinton N'Jie put Lyon ahead before Rose's red card, with the visitors capitalising on their numerical advantage with goals from Max Gradel - a penalty - and Romain Hamouma prior to half-time.
But Christophe Jallet's goal early in the second half earned a point for Fournier's side.
Fournier said his team never stopped believing, despite being behind at the break and down to 10 men.
"Sometimes football is a little weird. We conceded a goal on their first chance. It is a goal that hurts, that has halted the team dynamics," he said.
"We concede the second goal just before the half-time. It could have hurt us. At half-time, we felt that we were able to go for a draw or even victory."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
