The seven-time world champion ended up 0.501s down on polesitter Carlos Sainz at the Marina Bay track, while team-mate George Russell split the Ferraris to qualify on the front row.
The qualifying battle between the Mercedes drivers has been closely fought in 2023, with Russell inching ahead 8-7 in Singapore.
Hamilton scored the team's only pole position of the year in Hungary, his first since 2021, but it remains his only front-row start of the season to date, and he remarked in Monza last time out that he was "counting down the days until February" when the new Mercedes is launched.
Explaining that a set-up change overnight "didn't work for me" in qualifying, Hamilton said: "Really happy for George, I think he did a mega job. He's just been connected with the car all weekend.
"It started good for us yesterday and it's not so good today."
Asked how difficult the car was to get in the sweet spot, Hamilton replied: "It is the hardest car that I've ever driven to get right."
Hamilton believes Russell has "a really good shot at potentially winning" the grand prix on Sunday, with the younger Briton talking up the potential advantage that may result from having an extra set of medium tyres.
But Hamilton played down his own prospects of a strong result as he is unsure how the car will respond to the set-up changes over a long stint.
"For me, it's just - yeah. See what I can do," he said. "If I can get further up then great.
"The car was good yesterday on a long run but I changed the car overnight and it's now - I don't know what's going to happen tomorrow with the car."
Earlier in the weekend, Hamilton was critical of the decision by four teams to block the introduction of an additional DRS zone on the approach to the Turns 16 and 17 chicane as "teams should be for more racing, not against it".
Asked by Motorsport.com if he felt the race would be any better even without the DRS Zone, he replied: "I think so, just because of the track layout, the surface is better.
"I don't know if it's going to be a huge difference but hopefully it's in a positive direction."