The seven-times French champions, playing in the last four for the first time, had high hopes of reaching the final but they fell flat, losing 4-0 on aggregate to the Germans.
NEWS:Bayern brush aside Lyon
Claude Puel's side were never in contention in the second leg, being totally outplayed as they fell to an embarrassing 3-0 home demolition on Tuesday.
"Were they repressed by what was at stake? Did they just overthink? Maybe a bit of both. However they paid dearly for their lack of experience," Petit wrote on sports daily L'Equipe's website on Wednesday.
While they were up to the challenge in the first leg at the Allianz Arena, losing narrowly 1-0 to an Arjen Robben goal, Lyon failed to show the same character in front of their home crowd.
"There was no aggressiveness. When you are inferior, you have to bare your teeth," Petit, a former Arsenal and Barcelona player, added.
"You have to make up for your deficiency in the game with mental strength."
Lyon also cited Bayern's impressive play, with the French side failing to keep possession and being forced to chase for long periods.
"Even their injured players were running like rabbits on the pitch," said Lyon president Jean-Michel Aulas.
Lyon midfielder Maxime Gonalons said: "We were running after the ball and it took a lot of energy from us, physically and mentally."
Striker Lisandro Lopez, who has a reputation for being a tough character, broke into tears at the end of the game prompting Petit to wonder whether Lyon would be able to bounce back as they chase a Champions League playoff spot in Ligue 1.
"There could be a mental breakdown that would cost them a lot in the final sprint in the league," Petit said.
Lyon lie fifth in the standings, two points behind third-placed Lille, who hold the final qualifying position, but Puel's side have a game in hand.
"We must get back on our feet and do everything we can to be in a position to play the Champions League again next season," said winger Ederson.
Aulas agreed: "I know that we will have to be tough on Sunday (away to Montpellier). Lyon are a great team and great teams never die."
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