The McLaren driver performed well in tricky damp conditions to end up fourth fastest in Q2.
But when the track dried for the final session he ended up nearly three seconds off the pace.
Speaking after qualifying, Button said that the Q2 speed had flattered his car and reckoned reality would bite in the race.
"I'm very happy with our performance in Q2," said Button. "We should be pleased with what we did there. Being fourth with the car we have at the moment is good, I think. When it dries, we've haven't got the pace."
Button's plans to run a number of laps on the super-soft in Q3 means his tyres are now well past their best, which looks likely to further hamper his chances in the race.
"It's going to be really tough for me today," he said. "I did more laps than anyone on the option, which is our own fault.
"I didn't think the graining would be so bad but the rears are destroyed so it will be an interesting start - let alone the first few laps."
Button's team-mate Sergio Perez failed to make it out of Q2 after making an incorrect switch to slick tyres.
"I'm a bit disappointed but it was more unlucky because when we took the first set of options, I got a puncture on the rear left," he said.
"I lost a lot of time coming back to the pits. When we fitted another set of options there was no time left.
"I will be happy if today I can score some points. It's a big shame because today was a big opportunity for us to put the car further ahead than we are with our pace."