Ferrari fear Michael Schumacher could still miss out on his record sixth Formula One crown despite the German needing just one point from the last race of the season.
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"It would be a tragedy for us if we got that close and didn't win it," said Brawn.
"In many ways there is more pressure just to score one point than going into a championship when it is pretty equal."
Schumacher won Sunday's U.S. Grand Prix to take a nine point lead over McLaren's Kimi Raikkonen to the last race of the season in Japan on October 12.
An eighth-place finish at Suzuka will allow the German to overtake the late Argentine Juan Manuel Fangio in the sport's record books.
But although Schumacher has won in Japan for the last three years, Brawn feared history repeating itself.
"We've all got memories of Nigel in 1986," he said, referring to Mansell's final race of that year when he arrived in Adelaide with a six point lead only for a puncture to ruin his chances.
McLaren's Alain Prost won the title that year instead.
"It's going to be quite tough," said Brawn. "To go in needing one point is actually sometimes tougher than knowing you have to win it because there are so many things that can happen.
"It is going to be a very hard two weeks between now and Suzuka and we've got the constructors to try and win so we have to take our normal approach.
"To try and do anything different would be a mistake so I just hope the weather gods shine on us in Suzuka."
SWEETER SUCCESS
Schumacher's victory, the 70th of an astonishing career, allowed Ferrari to regain the lead in the constructors' championship with 147 points to Williams' 144.
It also ended the championship hopes of Williams's Colombian Juan Pablo Montoya.
Schumacher ran away with last year's championship, taking 11 wins in 17 races and wrapping up the title with six races to spare as Ferrari dominance ran riot.
Brawn said that a triumph this year, under new rules and against far stronger opposition, would be every bit as sweet - especially after Schumacher turned around a five-race losing streak to win the Italian Grand Prix two weeks ago.
"I know there are a lot of people who would like to see someone else win the championship and I understand that," he declared.
"But so many people have been supporting us and it was such a fantastic drive from Michael at Monza that it would be special to win it in more difficult circumstances and against much stronger opposition.
"It's not won yet so we are not counting anything yet. But it would be very special. You can never think a championship is a bit average. And this year, yes, it would be a bit special."
Brawn, who helped Schumacher win his two titles with Benetton before moving to Ferrari, said: "It was a great race and Michael showed his class today.
"Michael was really choked after the race and for a guy who has been in it a long time and won a lot of races...he still gets emotional when he wins a race so that is a wonderful thing."
Schumacher said after celebrating victory with his trademark leap on the podium that he wanted to secure the title with another win but Brawn took a more pragmatic approach.
"It's great. That would be a really special end to the season, but really you make decisions during a race," he said.
"You don't take chancy overtaking decisions in a race if you know you've got to score points."