Massa, who started on pole position for Williams at the Red Bull-owned circuit in 2014, will line up in 17th place while Canadian rookie team mate -- on the podium in Azerbaijan two weeks ago -- qualified 18th of 20 cars.
"We were immediately slow, starting yesterday," said technical head Paddy Lowe. "It was obvious that the pace wasn't in the normal ranking.
"We changed the balance of the car but we didn't actually make it any quicker.
"We tried a few more things going into qualifying which also didn't make it quicker. So the honest answer is we are not quick here but we don't know why."
The former champions, who last won a race in 2012, were by far the slowest of the teams with Mercedes engines at a track that has favoured the German manufacturer since it returned to the calendar in 2014 after a decade's absence.
Valtteri Bottas took pole position for Mercedes while team mate Lewis Hamilton and the two Mercedes-powered Force Indias qualified in the top 10.
Williams have brought aerodynamic upgrades to Austria and Lowe said the package had performed as intended.
"The long run pace yesterday didn't look too bad so hopefully it's simply a matter of single lap performance rather than general race performance, but I don't want to speak too soon about that," he added.
Massa, who might have won in Baku but for a suspension failure, said he had no answers either.
"It was the worst qualifying we had during the whole season," he said. "Really disappointed.
"Something is not working on the car. And we need to understand what.
"With the new tyres, I was just struggling to make the tyres work and lacking overall grip, especially in the front. It's very strange, difficult to explain... I don't think it's the package but something is not making the tyres work."
(Reporting by Alan Baldwin, editing by Ken Ferris)
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