The German was forced to retire two laps from the end when riding in third last time out in Italy, with team mate Lewis Hamilton taking the chequered flag to stretch his lead to 53 points in the drivers standings.
Rosberg, though, was adamant that there was still enough time to catch the British driver.
"I have the chance to keep believing or not and I have chosen to keep believing because it is going to help for the next couple of races and historically in sport anything can happen," he told reporters ahead of the race at the Marina Bay Street Circuit on Sunday.
"There are still seven races to go, lots of points, so keep pushing. With the car that we have its possible to win every race weekend which is a great feeling so focus on race weekends and then see what Lewis does."
Rosberg endured a difficult race in Singapore last year, retiring after 13 laps having been forced to start from the pit lane following problems with his car's steering and electronics.
That retirement allowed Hamilton to overhaul a 22 point deficit and go on to land a second world title as he won six of the final seven races with his trademark aggressive approach.
Rosberg said it was not yet time to change his racing style for the final races as he tries to emulate Hamilton's efforts last year.
"I want to win the championship," he said. "The feeling last year in Singapore was a lot better than now as I had 20 something points the other way. Much preferred that one."
Rosberg admitted his chances were not aided by his need for a fourth engine of the year -- Hamilton has only used three -- with a 10-place grid penalty looming if he needs a fifth before the year is out.
"New engine and we are not sure how compromising it will be yet, a small compromise at least or maybe a big one, we don't know yet," said the 30-year-old German, who anticipated a strong challenge from Ferrari and Red Bull in Singapore over the weekend.
(Editing by Pritha Sarkar)
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