McLaren racing director says first lap collisions involving the squad have masked the progress made by the team across recent months.
Fernando Alonso was running an upgrade package on his MP4-30 in Austria but he was eliminated exiting Turn 2 after he was collected by Ferrari's Kimi Raikkonen.
Alonso was also involved in a first lap collision in Britain, when he caused terminal damage to team-mate Jenson Button's car as he attempted to avoid earlier contact involving Daniel Ricciardo and both Lotus drivers.
Boullier believes that those incidents have restricted McLaren from showing its potential.
"We head to Hungary keen to shake off the poor luck we’ve encountered in recent races," said Boullier.
"It’s been a source of great frustration to see new components and upgrades destroyed before they’ve had the chance to be race-proven, through a series of first-lap accidents.
"However, the unshakeable belief and optimism of Fernando and Jenson has set the example for the whole team: they are remarkable assets, and their commitment during these times is incredibly valuable.
"Honda, too, has shown a commitment that remains admirably undiminished. Together, we are showing the fighting spirit and resilience that will see us continue to improve our performance and reliability as we move back to the front.
"I hope that our performance in Hungary will scratch the surface on the performance and potential that lies within our organisation – it would be great to go into the break feeling re-energised about the races ahead."