Zak Brown insisted that McLaren's papaya rules were made to be bent after Monza reignited the debate over whether team orders are needed at the British-based team.
Oscar Piastri and Lando Norris claimed second and third behind Ferrari's Charles Leclerc, with the latter enduring another poor start after securing pole in qualifying.
The Australian was able to make his way past his McLaren team-mate heading into Turn 4, with Piastri ultimately able to finish ahead of Norris at the end of the race.
However, McLaren recorded their fourth-best ever run of having one or both drivers on the podium (12), while also closing the gap in the constructors' championship.
The gap to Red Bull now stands at eight points ahead of Baku in two weeks, with Norris also closing the gap to Max Verstappen to 62 points in the drivers' championship.
But in allowing their drivers to fight, McLaren opened the door for Ferrari to pounce, but Brown defended Piastri's move on his team-mate in the opening exchanges.
“It was aggressive, it was an aggressive move [by Piastri],” Brown told Sky Sports F1 after the race.
“Their start was great and that was what we had discussed, kind of get behind the other and fan out to make sure nobody else could get by.
“I think Lando was caught by surprise with that move, thinking let’s just tuck into a one-two and see if we can pull a bit of a gap, so it’s something we’ll discuss internally.
“Papaya rules are it’s your team mate; race him hard, race him clean, don’t touch, that happened.
"It was an aggressive pass so that’s a conversation we’ll have, that was a bit nerve wracking on pit wall but it’s really just respect your team mate.
"Lando got a bad run out of that corner as well so it would have been nice to see them run one-two a bit longer.
"They didn’t touch, it was an aggressive pass but a clean pass.”
Despite McLaren's recent success, Ferrari's triumph at their home race has brought them back into contention for the constructors' championship and are just 31 points further back.
The British-based team have failed to win the title since 1998 when Mika Hakkinen and David Coulthard worked together to deliver their eighth constructors' title.
However, Brown remained firm in his assessment that McLaren would not prioritise one driver over the other for the remaining eight races of the season.
“They are both young drivers who want to win. We have always believed in having two number ones," Brown said.
"That’s always been McLaren’s way, it can be difficult to manage – we’ve seen it with Senna and Prost.
“They get along great, they do race each other clean and it’s philosophical – are you a one-car team or a two-car team?
"The easiest thing would have been for Lando to just run away with it, and then not have to put difficult decisions on the pit wall, but Andrea and I are taking it one race at a time.”