Quartararo inherited second in Sunday's 20-lap grand prix at the Circuit of the Americas when race leader Francesco Bagnaia crashed out.
For the first 12 laps of the main race, Quartararo fended off VR46 Ducati rider Marini but could do nothing to stop the Italian from outdragging him on the back straight on the 13th tour.
Quartararo had to settle for third, which marked his first podium of what has so far been a difficult 2023 season on a Yamaha that struggles under acceleration.
Though Yamaha ostensibly made top speed gains with its engine over the winter, Quartararo says it is hard to "be calm" when going up against Ducatis in a straightline.
"Long, tough race," Quartararo said after taking the chequered flag in third.
"We know our problem is especially on the power, on the acceleration, with the wheelie.
"So, we have many problems and I think in this track – Turn 11, Turn 1, Turn 20 – there are a lot [areas where you] wheelie.
"We need to make a step in that area. It's difficult to accept, but most of all it's difficult to be calm on the straights when you see a rocket ship coming.
"But to be honest, I was pretty calm and that's a good thing."
Quartararo's first podium of the season at the Circuit of the Americas came after he crashed out of sixth in Saturday's sprint race, with the Frenchman now 30 points off the championship lead.
Complaining after Saturday that the Yamaha had not made any major gains in the four years he has been with the marque and a radical overhaul would be necessary for 2024, Quartararo says his Americas GP result at least gives him some "self-confidence".
"I feel happy, especially for the team," he added. "I think it will bring a lot of motivation, a lot of self-confidence arriving to Jerez.
"So, yeah, I'm feeling happy and hopefully we can make a step forward soon.
"It's a big boost of confidence for myself, the team around us. I think what's positive is that, we are struggling, but at least to have a little bit of happiness in the team will be great after the celebrations."
