The 32-year-old Australian said: "I'm confident we can keep on producing but Jenson is not a guy who makes mistakes. He is incredibly consistent and he will continue to get points. So, effectively, we've got to close the gap in the next six races because he's got a two-race lead already. We need to get within 10 points with a race to go."
Button, 29, insisted he was at a disadvantage in the races in Britain and Germany because cool temperatures took the edge off his tyres which, on his particular car, work better in hotter conditions.
That is why he is looking forward to the Grand Prix in Hungary where he claimed his own maiden Formula One victory in 2006.
Button, suddenly on the back foot after winning six of the first seven races of the campaign, said: "It's going to be hot enough to make the tyres work, so we're going to be pushing the Red Bulls a lot more. And we need to start beating them, otherwise they'll take too many points off us. They've already taken 11 points out of me in two races. That's too many."
Button has also joined growing concerns over the Formula One debut in Hungary of Jaime Alguersuari, the Spanish prospect who at the age of 19 years and 126 days will become the sport's youngest-ever driver.
Alguersuari, the British Formula Three champion, has been brought in by Toro Rosso to replace Frenchman Sebastien Bourdais who failed to make the grade and was sacked.
He has never driven a Formula One car in anger and the technically difficult nature of the Hungaroring track means the rookie is being thrown in at the deep end, sparking some concerns that he may become a danger to himself and other drivers.
Button said: "Not having driven a Formula One car around a circuit, I'm surprised he's been allowed to race this weekend.
"If someone gives you an opportunity to race in Formula One, you're going to take it. But at his age it could absolutely destroy his career.
"If it goes well, then fantastic, but it's on a knife edge.
"It's not just about driving quick, I'm sure he doesn't understand all the electronics on a Formula One car.
"The steering wheel, to start with, is very complicated and to get the pit stops sorted in the two days of practice is going to be very difficult.
