The Ligue 1 side held Barcelona to a goalless draw at home but Lionel Messi produced a mesmerising performance with two goals and two assists in the return leg of the last-16 tie.
Messi opened the scoring from the penalty spot after Jason Denayer was adjudged to have brought down Luis Suarez, the decision of on-field referee Szymon Marciniak upheld by VAR.
But some replays appeared to indicate Suarez had instigated the contact by treading on the foot of the Lyon defender before theatrically going to ground in the box.
After Philippe Coutinho doubled Barca's lead Lucas Tousart gave Lyon hope of a fightback, only for Messi to run riot against a stretched back line and substitute goalkeeper Mathieu Gorgelin – on for the injured Anthony Lopes – in the closing stages.
And outspoken Lyon president Aulas was in no doubt that the decision to award Barcelona their penalty was key despite Bruno Genesio's side eventually falling to a comprehensive loss.
"It's hard when you miss your starting keeper, it's hard with that crazy penalty decision," Aulas said. "I remembered [former UEFA president] Michel Platini, who stood up against VAR.
"Lyon were not the best team, but the score doesn't reflect the game. You know I'm no football expert, I'm just the president of a provincial club. But there are two facts of play that made it really hard for us.
"Maybe if Messi switched teams, the result would be reversed. We will reinforce the team in the summer and we will try to be back in the Champions League."
Suarez himself cast doubt on whether the decision to give the penalty was correct in a post-match interview.
"I think I unintentionally stepped on him," the Barca striker said. "And I think after that he destabilised me. That's why the referee is there, he can whistle or not.
"We were great in the first half. We knew the opponent would push a bit more in the second half and after their goal there were five or 10 minutes when they grew a bit more, so it was important to kill the game off at 3-1 and relax."
Barca are into the quarter-finals for a record 12th season in a row and Suarez is not concerned he failed to get on the scoresheet, the Uruguay international still yet to find the net in this season's Champions League.
"I'm excited to get through," he added. "The team is growing in confidence and into the next round. It's true that strikers live for goals, but the goals will come."