The seven-times French champions were knocked out 6-3 on aggregate in the first knockout round by Barcelona after a 5-2 defeat in Spain on Wednesday.
Lyon have dominated French soccer this decade but last qualified for the Champions League quarter-finals in 2006. They lost to AS Roma in the first knockout round in 2007 and to eventual champions Manchester United at the same stage last year.
"Olympique Lyon are responsible for such a result but so is French soccer as a whole," Aulas told reporters.
"This game showed the gap between us and a club playing in a stadium such as the Nou Camp, which is far different from the one we have in Gerland, a club competing in a league starting in late August while we, in France, begin to play in July," he added.
Lyon plan to build a new 62,000 capacity stadium by 2013 but the project has long been delayed by red tape.
Aulas also said high taxes prevented French clubs from winning the Champions League as they cannot pay wages as high as those offered by their European counterparts.
"French soccer needs to make progress regarding its tax system because everybody saw that the best players wore the Barcelona jersey tonight," he said.
France striker Thierry Henry scored a double to help Barcelona open a 4-0 lead over Lyon after only 43 minutes on Wednesday.
"We have to draw conclusions from this defeat, not only us but French soccer as a whole," Aulas said.
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