It was the first time since the 2009 Abu Dhabi season-ender that a Ferrari had started at the back of the grid on performance.
"I feel terrible," seven-time world champion Hamilton, who made his debut with McLaren in 2007, told Sky Sports television in the immediate aftermath, before both McLarens were disqualified.
"It's been the worst season ever. No matter how much I try, it just keeps going worse.
"I've tried everything, in and out of the car."
Hamilton, who joined from Mercedes in January, has yet to stand on the podium in 22 races for the Italian team - with a sprint win in Shanghai in March the only real bright spot of the campaign.
Ferrari are the only top four team without a win in 2025 and have slipped from close second to McLaren last year to fourth in the standings.
"I don't even know how many points we have, but at this rate, with my performance, we're done," Hamilton, who cannot now finish the season in the top five overall, told reporters.
Hamilton has sounded increasingly gloomy about the team's performance after upbeat comments early in the season, with Ferrari chairman John Elkann recently saying the drivers should talk less and focus on driving.
On Friday, Hamilton described qualifying as horrible, and team boss Fred Vasseur said he knew where the Briton was coming from, but told him to focus on working with the team to improve things.
"I can completely understand the adrenaline and the emotion and having a comment that is a bit harsh at this stage of the weekend," he told reporters.
"The most important thing is not what they say in the TV pen, it's what they do on Monday morning with the team to try to do better and try to push the team to do better."
Former teammate and 2009 world champion Jenson Button, now a Sky television pundit, sympathised with Hamilton.
"It's been a very difficult season for someone of his calibre. He's carried himself so well," said the Briton.
"It's the first time I feel we've really seen him seriously deflated. It gets to you. Mentally, it's draining when you have a few bad races.
"It won't weigh on him after this weekend, but it's a tough moment for his career right now."