The Brazilian had started sixth, but made a poor start to drop to ninth by the end of the first lap - and then lost ground rapidly to those in front, lapping between one and two seconds slower. That prompted an early switch to the medium rubber, on which his pace improved rapidly - but he was then bottled up behind Force India's Sergio Perez, which restricted him to sixth at the flag.
"I'm not happy - I would say maybe the first 10 laps were a disaster for us," Massa said after the race.
"The start was not good, but also the pace on the soft tyres was really a disaster, we lost many positions - both cars. It was really tough for us.
"I'm sure it [influenced] a lot the result at the end of the race, this problem I had at the beginning. So I'm not happy. The race could have been completely different."
Valtteri Bottas meanwhile lamented a pit stop error in which he was fitted with three softs and one medium tyre - which earned him a drive-through penalty and squandered what he believes was a shot at the top four.
"Disappointed, that's the best word - I think everyone in the team is," Bottas reflected after finishing ninth.
"Not the result we were looking for, for sure. I think I lost five places at least with the penalty today, not ideal. The pit stop and the race pace are two areas that we need to investigate. We thought we would be stronger during the race but the soft tyre in the first stint didn't work as well and put us in a difficult position. We have to make sure we bounce back well in Monza."
Bottas was not the only man who felt a possible podium had slipped through his fingers - Daniel Ricciardo was also left to bemoan his luck after technical issues brought his race to a halt while running fifth. On a similar strategy to Daniil Kvyat, who charged through to snatch fourth late on, Red Bull felt that denied him a clear shot at the podium.
"It's a shame for Daniel; he had a great start to move up to third," team principal Christian Horner said. "He was running a similar strategy to Dany and I'm sure he would have been challenging for the podium. It was a lost opportunity but overall a reasonable weekend for the team."