Button was 11th fastest in practice at Silverstone on Friday, and sees no prospect of the weekend turning around given McLaren's ongoing struggles.
"The car doesn't feel too bad out there, we're just slow," he said.
"On the straights we don't have the issues we had in Canada, so that's good.
"But we're still going to be a long way from the front.
"I think we can improve a tiny bit, but I think Q3 is a long way off for us this weekend.
"I'm one and a half seconds off the quickest car, so there's good reason to be disappointed."
His team-mate Sergio Perez was more optimistic, feeling that the new parts McLaren added for Britain are an improvement - albeit not a sufficient one.
"We did another step but still we are quite far off," said Perez.
"I think we can improve more for tomorrow but we're in a similar position to Canada.
"We can aim tomorrow for Q3 if we get the perfect lap."