'High stress' at McLaren with first F1 constructors' championship since 1998 in sight
McLaren lead the standing with 593 points, 36 ahead of Ferrari with defending champions Red Bull still in the running with 544 points ahead of Saturday's Las Vegas Grand Prix.
"I feel great with where we are," Brown said at an event promoting the British team's partnership with Mastercard.
"But it's high stress. A 36-point lead can evaporate in one race weekend when you've got Ferrari, who could easily finish first and second, which can happen in a street race as we saw in Brazil.
"For those people who have come up to me with a foregone conclusion that we've already won the championship, I kind of want to punch them in the nose."
McLaren team boss Andrea Stella said the constructors' championship was the priority after Lando Norris finished sixth in Brazil earlier this month, putting Red Bull's Max Verstappen on the brink of a fourth successive drivers' crown.
There are two more races to go after Las Vegas and the constructors' championship could go down to the wire in Abu Dhabi in December.
Ferrari team boss Fred Vasseur said recent results had little bearing on who would come out on top.
"It's not a matter of momentum this season," he told reporters after Thursday's first practice.
"If you have a look, I think Red Bull were dominating the first three or four races at the beginning of the season. Then we had a good sequence and then it was Mercedes during the summertime and then it was McLaren again and us again.
"It's so tight that it's moving from one weekend to another."
Brown said staying consistent will be key to locking up the title.
"A lot of people have asked what we are doing differently now," he said.
"We don't want to do anything differently. We want to do exactly what got us to where we are. Take it one session at a time, feet on the ground.
"The minute you think you've done it before you're in the end zone is a big mistake to make.
"So I feel good about where we are but we're very focused and we're not going to celebrate until hopefully we've earned the right to celebrate."
