The Monegasque spun out midway while leading the pack at Circuit Paul Ricard, allowing rival Max Verstappen to notch up another win at his expense.
The Red Bull driver has taken advantage of Leclerc's errors before this term, as he seeks to make it a second consecutive drivers' championship crown, and now sits 63 points ahead of the latter.
Hamilton also capitalised on the Ferrari driver's misfortune to post his best finish of the season after a difficult campaign battling with a below-par Mercedes car since the start of the year.
But the seven-time world champion believes Leclerc will bounce back thanks to Ferrari's impressive form, adding that he understands the struggles his fellow driver is going through.
"It's been great to see the pace of the Ferrari this year," Hamilton stated. "I'm gutted for Charles, who's being doing a great job, as has Carlos [Sainz].
"It's not easy, though, having that pace and that performance and maintaining it. It's a tough job and I feel for the whole team because I know what that can feel like.
"But they're a great team, and they'll continue to keep their heads down."
Ahead of the Hungarian Grand Prix – the final race before the mid-season hiatus – Hamilton is feeling buoyant following a fourth podium finish in a row.
While he still feels Mercedes will not be able to mount a challenge to upend the latter half of the season between Red Bull and Ferrari, he is brimming with confidence on how their experiences can shape their approach to 2023.
"I know exactly what I want in the car for next year," he added. "Things that fundamentally can't change [this year], because it's too big to change here with a cost cap this year.
"So I'm able to – ahead of time – say these are the things I want in the next year's car.
"Those things are being taken into account and whilst we continue to try and dial this car in, of course bit by bit, as we go into these next weeks, the next couple of months, the full focus will probably be into next year's car."