Garcia concedes his captain was not 100 per cent match fit but hoped the inclusion of the team's star player could inspire his players to victory.
"I chose to start Dimitri, one of our best players," explained Garcia. "Even diminished, he set up a chance for Valere Germain.
"We missed him from set-pieces as Atletico, if they do ever concede, sometimes concede from set-pieces. We hoped that he'd be at 100 per cent and we gave him a fitness test this morning.
"He was worried about playing and whether he'd be able to kick the ball hard.
"He didn't aggravate the injury today, he just wasn't fully fit. In matches like this you have to take risks."
Marseille were 1-0 down when Payet was forced off after Atleti pounced on a poor touch from Andre-Frank Zambo Anguissa for Antoine Griezmann's opener.
Olympique Marseille (@OM_English) May 16, 2018
But Garcia insists culpability for that goal should be shared with Steve Mandanda, who played the heavy pass to Zambo Anguissa, adding: "It was 50-50."
Griezmann's second doubled the advantage for Atleti, before Gabi netted their third a minute from time.