The Briton, second in the championship, finished fourth on track but ended up fifth behind teammate Charles Leclerc after a five-second penalty was added to his time for speeding in the pitlane.
He had been running in second place before the pitstop, taken during a virtual safety period moments after McLaren's Oscar Piastri had pulled over and retired with a gearbox problem.
"I definitely don't think we should have taken a stop. The call came literally just before the pit lane entry and I didn't have time to debate it," Hamilton, now 50 points behind Mercedes' championship leader Kimi Antonelli, told reporters at the Hungaroring.
"You've got to trust the decision that has been taken but, in hindsight, my tyres were totally fine. I was probably going to lose out to Max (Verstappen), but I think I could have kept third at least. And it just opened up the door to the penalty that I got at the end."
Red Bull's Verstappen finished second behind McLaren's winner Lando Norris with Antonelli a close third. Both stayed out during the virtual safety car.
'Just can't catch a break'
Ferrari boss Fred Vasseur defended the strategy and said it would have been unfair to ask Leclerc to increase the gap to preserve Hamilton's position at the end.
Hamilton, a record eight-time winner in Hungary, had arrived hoping to secure his first pole position since 2023 at a circuit that looked likely to favour him and Ferrari.
Instead, he missed out on pole by 0.012 of a second to Norris and was then demoted three places - the latest of a string of penalties that has come his way in recent races - for impeding Piastri, a big blow to his hopes at a track where overtaking is tricky.
"Sometimes you just can't catch a break," he had lamented on Instagram on Saturday.
"Another weekend when I've been feeling great throughout all the sessions, but then it just falls apart."
That proved prophetic, with fifth so much less than the 41-year-old had hoped for.
"The last three races have been pretty bad from my side," he said.
"At the last race (in Belgium), even the driver I collided with (Mercedes' George Russell) said it was a racing incident and they gave me a penalty. That was not needed. And that’s cost me a lot of points. Yesterday was unfortunate. I take responsibility, I should have looked in my mirrors.
"I will work hard to come back, reset, and there are still lots of positives to take. But I have to make sure I don’t give them (the stewards) any reasons to give me a penalty.”