In Austin, Norris was given a five-second penalty for going off the track and gaining an advantage trying to overtake Verstappen. The Briton refused to give the place back after Verstappen complained, highlighting he had been ahead at the apex. The stewards, however, disagreed with Norris.
Many drivers made it clear they felt Verstappen’s driving was not fair in Austin and told the FIA that the racing guidelines needed changing to address the type of tactics the Dutchman had employed.
A week later in Mexico, the two drivers clashed again, with Verstappen being given a combined 20-second penalty for two incidents with Norris on the same lap. Norris called Verstappen's driving "dangerous" and flagged again that he was ahead of the three-time world champion into the corner during the first tussle.
"I think we need to take a step back and not over-regulate what happens on the track. We never used to do that in Formula 1," said Brown.
"I think we’re racing too much to a rulebook now versus good old fashioned racing - just give the stewards a little bit more discretion. They’ve raced, they know that a driver has been pushed off or not, or made a lunge, or not. And not have this black and white rulebook."
However, Brown says he does have confidence in the governing body's president, Mohammed Ben Sulayem, following the departures of senior members of FIA staff in the past year.
Race director Niels Wittich, a replacement for Michael Masi in 2022, left his role with immediate effect on 12 November, with less than a month of the season remaining.
Wittich was said to have "stepped down" but he told BBC Sport last week: "I can confirm that I got fired and it was not my decision to leave F1." The German has been replaced from this weekend's Las Vegas Grand Prix by Rui Marques.
"He doesn't mess about. He makes decisions," Brown said of Ben Sulayem. "I think we were surprised by that decision, more the timing of it."
McLaren are top of the constructors' standings by 36 points with three races remaining and Brown says "it would be unbelievable" if the team could secure their first team title since 1998.
"It's hard to believe it was that long ago," he added. "That's why we're here. We're here to win world championships."