The principality club sit second bottom in Ligue 1, three points from safety after winning just three of their first 17 league games.
And a very unhappy Henry laid into his players following their 10th defeat of the season, criticising the fight his side showed on the pitch.
"Against Dortmund (in the Champions League), I said, even if we knew we were already eliminated, I'm really upset because you cannot lose like that. Tonight, we did exactly the same thing," Henry said in France Football .
"Look at the first two goals. On the first goal, we give them the ball for free.
"The second goal sums up the match for me. A pass of 35 meters I think from Denayer between two players. I cannot understand how that pass happens. Then there's a guy who wants to focus, to score and one who does not want to defend.
"You can play four or five defenders but with a lack of desire, it's hard to win a football match. It was a lack of desire tonight on the goals. So, no excuses, no excuses.
"I think we made life too easy for Lyon. On the goals, we are at fault. We made the match too easy. It's a heavy, hard defeat. Above all, when we make too many mistakes, a team like Lyon, which has many qualities, will score goals.
"We will have to do what there is to do against Guingamp and try to get out of the relegation zone before going on holiday."
He added: "But try to stay a little on what we did in Amiens and Caen. I know that when you play against a team like Lyon, you find yourself immediately in trouble when you make this kind of mistake, as we are well aware. But we try to stay positive anyway.
"I see the team every day in training. I do not feel that it is the desire that is missing. But I think that maybe in our situation, it's the head that makes us make mistakes. On the field, we do everything to win.
"You have to work hard and not give up. For me, it's still a very bad signal when people after the match ask me if the team wanted to win. That must be changed very quickly."