Hamilton, second in the drivers' championship to Mercedes team-mate Nico Rosberg, had dominated free practice on Friday and Saturday only for his qualifying session to end after five minutes.
The Briton was on his first warm-up lap in Budapest when flames began to emerge from the back of his car, forcing him to pull up before the pit lane.
Hamilton has now been struck down by mechanical problems on four occasions this season, and is eager to avoid any further issues.
"There's a lot going through my mind, but I just have to try to turn it into positives until tomorrow [Sunday]," he told BBC Radio 5 Live.
"I think it's getting to the point beyond bad luck - it's something else. We just need to do better.
"We'll have to replace the engine and gearbox, but with that penalty it's a good thing - I can't go any further back [on the grid]."
With overtaking difficult in Hungary, Hamilton, who will start at the back of the grid on Sunday, could find himself further behind Rosberg heading into the mid-season break.