Despite a spirited performance, Garde's men were beaten 2-1 at Juventus Stadium, handing the Italian champions a 3-1 aggregate win.
Lyon were given hope when Jimmy Briand responded to Andrea Pirlo's early free-kick by levelling the tie, but Claudio Marchisio's 68th-minute effort took a decisive deflection off Samuel Umtiti to send Juventus through with a degree of comfort.
Garde took a number of positives from his side's display, yet conceded Juve deserved to progress.
He told reporters: "I have no regrets for this game, though maybe for the first leg.
"The three goals (across both legs) were a little unusual. Andrea Pirlo's free-kick was marvellous, but we conceded in the first leg at the 85th minute and today Claudio Marchisio scored with a deflection.
"I would've preferred Juve to show their superiority with better goals, but we cannot have regrets really. The best team won.
"At half-time we thought that we were getting close to a huge achievement, because we only needed to score one more goal and knew we'd have chances after the break.
"There are always regrets when you go out of a competition, but we have to recognise Juve's superiority, even if over the two legs we didn't see that much difference between the teams. I must say I'm proud of my players."
A decent performance came despite Lyon coming into the game without a host of first-team players, leaving Garde to ponder what might have been had he had a full-strength side at his disposal.
"What were we missing? Maybe half of our team, even if I can't complain about those who played tonight," he added.
"We would've had other solutions in recent games and perhaps reached this tie with fresher legs."
