It depends how fast the planet depopulated. In Mad Max the original problem was water shortages. If most of the population was wiped out in the water wars, it’s reasonable that the dregs of fuel in the system could last the few survivors a long time.

In case of dragons there might also be helicopters around.

I guess the idea that cars would be around after the apocalypse comes from the diesel engine, which can basically run on vegetable oil.