Manchester City, who overcame Real Madrid in Friday's other fixture, await the Ligue 1 side in the last eight on August 15 in Lisbon, and the result left former Roma coach Garcia reveling in his team's success.
"It's one of the most satisfying moments of my career and getting past Juventus really is an exploit," Garcia told Sky Italia.
"The penalty we conceded just before half-time hurt us, Juve hadn't been that dangerous until then and it gave them confidence.
"Ronaldo then scored that real Champions League level goal, but we stayed calm and that was what I appreciated the most about my team. We didn't panic, we kept plugging away and everyone contributed to keeping the ball.
"I know this stadium, I came here with Roma, so I know how tough it is to win here. Let's just say this is the happiest defeat of my career!"
Garcia was not a universally accepted appointment at Lyon, with the Frenchman having coached rivals Marseille between 2016 and 2019.
He guided Lyon to a seventh-place finish in Ligue 1 in 2019-20, with France's top-flight ended early due to the coronavirus pandemic.