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Ferrari are just three points clear of Formula One champions Renault with three races remaining.
"This was not a good day for me," said Massa, who sat out the day's opening practice session and then suffered the engine problem in the afternoon that led to the unscheduled change.
"It's a shame as the car seemed to be well balanced right from the start and I had been able to do some good times," added the Brazilian, a first-time winner in Turkey last month.
"Of course dropping 10 places on the grid will make my race much tougher, but I believe I can still put in a good performance."
Massa's team mate Michael Schumacher is fighting world champion Fernando Alonso for the drivers' title with the German two points adrift of his Renault rival.