The 34-year-old was set for a top-six finish at the notoriously demanding race before a car failure robbed him of a strong result.
His future in the sport has been the subject of speculation for several months, with Fernando Alonso and Sebastian Vettel being linked to his seat at McLaren when Honda come on board as engine partners next term.
The Spaniard's name has been particularly closely associated, despite his frequent denials that he intends to leave Ferrari at the end of the season.
And Button now sounds increasingly confident that he will be back at the Woking-based team next year. When asked about his future after the Singapore race, the 2009 World Champion was calm.
“I’m not worried in any way about that. I’m pretty happy I’ll be here [at McLaren] next year, and I feel I’m doing a good job right now," said Button.
However he added that he needs to up his game in qualifying, with young team-mate Kevin Magnussen becoming increasingly dominant over one lap.
"I just have to sort Saturdays a bit more," said the Brit. "I’ve been a bit unlucky and not got the best out of it every weekend, which annoys me more than anything else, but I’ll get there."
Button also admitted that he expects 2015 to be a challenging year as McLaren adjust to their new engine partners after 20 years with Mercedes.
“I know Honda will be giving everything to be competitive from the word go, but Formula 1 is so competitive now, and Mercedes have done a great job," he said.
"It’s always going to be tricky to challenge someone like that who already have the experience of the engine. There will definitely be a learning curve.”
McLaren bosses Ron Dennis and Eric Boullier have indicated that they will make an announcement on their 2015 line-up before the season finale in Abu Dhabi next month. Magnussen looks set to hold on to his seat alongside Button, though both are likely to be handed one-year deals, with the likes of Vettel, Alonso and former McLaren star Lewis Hamilton all potentially on the market in 12 months' time.