The Italian acknowledged that at one stage there was a possibility that the Australian might have missed some of Saturday's sprint day track action in order to focus on being fit for Sunday's main event.
In the end, Piastri greatly impressed the team by not only completing the weekend but also finishing a respectable 11th in the race.
"We have had a couple of points during the weekend in which we needed to evaluate 'Is it better to rest now to make sure that we are okay on Sunday?," said Stella when asked about Piastri.
"So I can certainly admit that we have made this evaluation a couple of times, we've been very well supported by our team doctor.
"And the overall medical support I would like to acknowledge has been excellent in assisting Oscar, like his team.
"But Oscar has always been very calm, and 'Okay, let's try, I'll get in the car. If I can't do it, I will box.
"And then he has always found the resources to go through the session. But yes, a couple of points we thought, let's think that we want to be okay on Sunday, not now."
Stella admitted that the nature of the Baku street track made it even more stressful for Piastri, who was the only one of the three F1 rookies not to have a big accident during the weekend.
"It's one of the hardest, because of how close you go to the walls," said Stella.
"And it's a moment that you touch the wall like we've seen many drivers have this weekend in terms of even drivers in top cars, so it's definitely an issue that requires a lot of competent lucidity, and a lot of concentration.
"And sometimes Oscar kind of after a session said, 'I'm really exhausted.' It was interesting, he was okay in the session, and then after kind of a little bit of a drop."
After the race, Piastri put on a brave face while admitting that it had been a difficult weekend.
"I'm not too bad," said the Australian. "I think the adrenaline's still kicking at the moment. But I felt a bit better this morning, which was good.
"And I think through the race, it didn't impact me too much. I'm a lot lighter than I was at the start of the weekend.
"Today's probably been the best I've felt all weekend, which isn't saying much. But yeah, it's been very difficult physically. Especially yesterday, it was pretty rough.
"I think I've had about four pieces of toast for the whole weekend! So I may need to get some food back in me before Miami."
