Vergne was left without a drive for next year after Red Bull elected to promote Max Verstappen to a full-time Toro Rosso seat alongside Daniil Kvyat. Vergne, however, believes his strong Marina Bay result - achieved despite two five-second time penalties - should convince rival F1 teams of his ultimate potential.
“I am extremely happy, especially the way we took sixth place with the two penalties - amazing,” the Frenchman said after the Grand Prix.
“Ten seconds is a lot in the race - I really had to go and take those positions in the last laps and pull away as much as possible. Having to overtake so many cars was a lot of fun. To finish sixth was incredible.
“When you have a good car, that’s when you need to show yourself, and that’s hopefully what I have done. I think I showed my potential - I did everything I could. Let’s see if it might change things.”
Vergne also pointed to his strong record against Daniel Ricciardo when the pair were team mates at Toro Rosso as another measure of his credentials, particularly given Ricciardo’s breakthrough season in the Red Bull this year.
“When you see what Daniel is doing in a good car, winning races - I can do the same,” he added.
“When you are motivated and really want a result, that is what you do - I have shown this in the past, but when you overtake for 13th position they don’t put it on TV. That’s what I do at the back of the grid; when I have a good car like [on Sunday in Singapore] that’s what I do. But I need a good car to show myself, and to have people trust in me.
“I cross my fingers to keep a seat next year, and in a good team; I really hope so. We have an update for Japan, so I think it is good for me - the end of the season is where I need to push for next year.”
Vergne currently lies 13th in the driver standings, with 19 points, 11 ahead of rookie team mate Kvyat. He finished the 2013 campaign in 15th, directly behind then-team mate Ricciardo.