The 2021 world champion enjoyed one of his better weekends of an otherwise tough campaign at the Buddh International Circuit.
Quartararo was sixth in the sprint on Saturday and scored his second grand prix podium of the year on Sunday after trailing a dehydrated Martin home.
The Yamaha rider was able to close right in on Martin in the latter stages after the Pramac rider was forced to zip up his leathers, before Quartararo overtook him on the final lap when Martin ran off track at Turn 4.
Quartararo’s stint in second, however, lasted all but one corner as Martin carved around the outside of him into Turn 6 and held firm through the last few corners.
The Frenchman waved his hand in frustration when he crossed the line behind Martin, but explained that this was not directed at the Pramac rider.
“To be honest, when he overtook me from Turn 5 to Turn 6, clearly the grip I had on the left was really bad and I could not do anything,” Quartararo said.
“Even arriving to Turn 10 I was there, but the grip I had going in and on the brakes was really bad and I could not stop.
“So, we finished in P3. We clearly know where we are losing a lot of time on this track; acceleration, top speed and the grip we have.
“So, we have to work hard to fight these guys.
“It was ok [Martin’s overtake]. It was frustrating because I tried to make the best exit as possible, tried to be straight, but they just broke away with the grip. So, hopefully we can find a solution as quick as possible.”
Quartararo conceded third was “the best we could do” in India due to his grip issues, and stressed Yamaha must be “clever” in similar circumstances going forward to extract similar results.
“It was a great weekend overall, especially our pace in qualifying,” he added.
“So, I’m pretty happy about this weekend. Hopefully we can do many more this year.
“So, we have to be clever and as soon as we have small opportunities to make these kind of results we have to take it.
“I was struggling a lot to stop the bike, especially on the left corners. But we have to be happy with this podium.
“I didn’t know if it was arm pump or the leathers [that Martin was struggling with], but I saw he was doing something strange in Turns 10/11, and so I tried to push till the end.
“But I was feeling so on the limit with the feeling and tyre. That’s the best we could do this weekend.”