The Australian went second, after Norris was slowed by a late pitstop problem, but gave the place back as requested -- trimming his overall advantage to 31 points with eight rounds remaining.
"I think today was a fair request. Lando qualified ahead, was ahead the whole race, and lost the spot through no fault of his own," Piastri, winner of seven of 16 rounds so far, told reporters at Monza.
"I'm not going to go against the team. I think there's a lot of people to protect and a culture to protect outside of just Lando and I. Ultimately that's a very important thing going forward."
The 24-year-old had said initially over the radio that he thought slow pitstops were a part of racing, and was not aware anything had changed.
He had nothing to add on that but said the request had not come as any shock.
"We have had discussions about all kinds of scenarios and when you're in the same team, when there are things outside a driver's control, there's a lot more ways you can rectify things," he said.
"So it is a discussion we've had. I'm sure we'll review it and discuss more, but it wasn't a situation that hadn't been discussed before."
Norris, who had started on the front row alongside Red Bull's eventual winner Max Verstappen, said he would have done the same as his teammate and rejected a suggestion that a precedent had been set.
"We're not idiots and we have plans for different things. If there were four cars in between me and Oscar, of course he's not going to let me back past, and I don't think it's correct that he let me back past," said the Briton.
"But in a situation where we weren't racing, in a situation where we can just be fair, then you'd expect to be fair, as a team."
Norris, who suffered a mechanical retirement in Zandvoort last weekend, said McLaren did not want to be the cause of a driver's misfortune and it would have been different if the slow stop had been his fault.
"If I came flat-out into my box and I hit all my mechanics out of the way, I also don't expect to get the position back, but today was out of my control," he said.