Vettel leads the World Drivers' Championship by 85 points from his Red Bull teammate Mark Webber with eight races in the season remaining.
The 24-year-old German was world champion last year and is bidding for a second successive title.
"He's already won the World Championship, which is very important. You don't feel the pressure so much, when you've already done it," Button, who won the 2009 World Championship with Brawn, told The Independent.
"It wasn't easy for me to win consistently by the end of the year but he still has a massive lead. He has no need to take risks and he's driving a competitive car.
"Red Bull has great resources, so it's a different situation to the one I found myself in with Brawn. And if I had the lead he's got, I wouldn't be feeling any pressure at all."
The Formula One season continues with the Belgian Grand Prix on Sunday, August 28.