F1 and its governing body have found themselves on the receiving end of a wave of criticism for the way in which the 2021 season ended in controversy after the way a late-race safety car restart was handled at the final race.
While an FIA investigation into the events of Abu Dhabi and questions over F1's decision-making process is ongoing, Brown says the lessons of 2021 show that change is needed.
He says that the arrival of new FIA president Mohammed Ben Sulayem offers a great opportunity for a much-needed new approach that could avoid the kind of "pantomime audition" scenes that F1 descended in to last season.
Writing on McLaren's website, Brown said: "It is clear that some of the rules and their governance are not acceptable as things stand. No one is happy with the inconsistency in the policing of the regulations, but which has been habitually exploited by teams for competitive advantage.
"I have said before that the teams have too much power and it needs to be reduced. We have a significant role in the drafting of the regulations and governance of Formula 1 and that influence is not always driven by what is best overall for the sport.
"Yes, teams should be consulted, and their informed perspectives considered, particularly on long-term strategic issues. But at times it has seemed the sport is governed by certain teams.
"Let us not forget that we, the teams, have contributed to the inconsistencies in the policing of the regulations as much as anyone. It is the teams who applied the pressure to avoid finishing races under a Safety Car at all costs.
"It is the teams who voted for many of the regulations they have complained about. It is the teams who have been using the broadcasting of radio messages to the race director to try to influence penalties and race outcomes, to the point where an over-excited team principal plays to the gallery and pressurises race officials.
"This has not been edifying for F1. At times it's felt like a pantomime audition rather than the pinnacle of a global sport."
Previous FIA president Jean Todt pushed his desire to rule the sport by consensus, which meant a lot of consultation and influence from teams in laying down the rules.
Brown is clear in his hope that Sulayem will handle things differently, and thinks the time is right to do so now that F1 has changed for the better under new owners Liberty Media.
"The election of Mohammed Ben Sulayem last December as the new president of the FIA provides the opportunity for collective reform of the way Formula 1 operates," he said.
"It is obvious to focus on the events of Abu Dhabi at the end of last season, which are the subject of an FIA investigation, but this was a symptom rather than cause in my view. There have been systemic issues around alignment and clarity on who makes the rules – the FIA or the teams – that have manifested themselves in the past couple of years, at times in a high-profile way.
"The signs of organisational difficulties could be seen at the 2020 Australian Grand Prix and at last year's Belgian Grand Prix, both hallmarked by a seeming lack of preparation for the events unfolding and temporary inertia on the solutions.
"Greater clarity on the roles of the FIA and F1 and the need for increased leadership of the sport will undoubtedly be on the agenda for Mohammed Ben Sulayem and Stefano Domenicali and their respective teams.
"Previous administrations pursued a mainly autocratic style of governance, so to point the sport in the right direction it was necessary to take a more consultative approach with teams and stakeholders.
"But now the sport has been successfully reset, moving forward there is a need to shift back to stronger, more directive leadership and governance at the top of the sport."
He added: "I am confident that we will see increased leadership from the FIA and F1, and that collectively as custodians of the sport we will focus on evolving the sport and not shirk responsibility when it comes to tough decision-making."