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.
Source: Autosport