Although McLaren and Button had played down expectations for the developments introduced at Barcelona, the hope had been that the revised car would at least be a comfortable Q3 qualifier.
Yet while Sergio Perez got one McLaren into the top 10 in ninth, Button was left back on row seven. He felt a tyre pressure error had caused his woes.
"The tyre pressures were massively high, so I don't know if something was wrong or if they were set wrong, but we're looking into it now," Button said.
He said the upgrades had been beneficial, but not sufficiently.
"They're making a little bit of a difference but nowhere near enough to really challenge up the front," Button said, "and everyone has got new parts so it makes it very tricky for us to catch up."
The Briton took some solace from Perez's performance.
"The good thing is the car with Sergio in it has shown we have made some progress, which is what we need and we need to build upon that," said Button.
But Perez was far from happy despite reaching Q3.
"To be in Q3 with a difficult car makes me feel OK," he said.
"As a driver in a winning team like McLaren you want to be at the front. But in the end you have to be happy when you maximise everything."