Norris backtracked on Thursday on his call for the Dutch triple champion to apologise for a costly Austrian Grand Prix collision that came while both were fighting for the lead last Sunday.
That U-turn was followed by Verstappen, whose uncompromising style has been much discussed outside his team, emphasising how much he valued the relationship with his friend and did not want to ruin it.
Some saw that as Norris handing Verstappen a psychological advantage by defusing the situation rather than keeping the pressure on.
The pair have been first and second in five of the last seven races, with Verstappen winning seven times in 11 and Norris once.
"I think there's a difference between what a racing driver's like when the helmet goes on and the visor goes down, and what they are like Monday through Thursday and how they communicate and carry themselves in the relationships that they have," said Brown.
"A lot of world champions (are) sweethearts outside of the race car but pretty fierce once the helmet goes on and Lando's no different."
Brown described the battle between the two as 'epic' and said Verstappen, like any great driver or top designer, would naturally push the rules to the limit until he was told he had gone too far.
The American, who repeated his call for permanent stewards, was not letting Horner off any hooks, however.
The Red Bull boss told Verstappen over the radio on Sunday that Norris had not behaved correctly.
Stewards saw it differently, blaming Verstappen for the collision and handing him a 10-second penalty and two penalty points.
Brown said he was "disappointed that at such a great team like Red Bull that the leadership almost encourages it because you listen on the radio and what was said.
"We all have a responsibility on pit wall to tell our drivers the do's and don'ts and what's going on in the race and so I think we need to have respect for regulations.
"And we've seen there to be a lack of respect, whether it's financial regulations or you know sporting, on-track issues with fathers and things of that nature, and I just don't think that's how we need to go racing and we need to guide our drivers on what's right or wrong."
"I think had it been addressed earlier maybe that incident wouldn't have taken place."
Champions Red Bull were fined $7 million in 2022 for breaching the cost cap in 2021 while this year Horner has fallen out with Verstappen's father Jos and faced allegations from a female employee of misconduct.
The boss denied the allegations and was cleared after an investigation.
