An equaliser 10 minutes from time from Ibai Gomez looked set to have earned the visitors a draw until Jimmy Briand secured a dramatic win for the French outfit thanks to his winner five minutes before the final whistle.
Bielsa lamented his team's late lapse in concentration to concede the goal, believing that, on the balance of play, his side should have come away with at least a point.
“We had 85 minutes of domination but we suffered a bad five minutes and that cost us the match," the former Argentina boss said at the post-match press conference.
“Our equaliser had more of an effect on Lyon than it did on us and that is hard to understand.
“We could not defend well because we were disorganised and that's why we didn't win. Maybe a bit more aggression would have put the game in our favour.”
The defeat leaves the Spaniards in real danger of not qualifying for the next round after just collecting one point from three matches, but Bielsa promises that his team will continue to fight.
“After obtaining a single point out of nine, we can't be optimistic. But we need to win our next three matches so we can't give up now," he concluded.