1,500 years after the apocalypse, civilization has finally got back on its feet. The only thing they don’t have is cars. Why might civilization not reinvent automobiles?
Superstition or Cultural reasons
In Stephen king's Dark Tower series the descendants of the the survivors live in feudal style structure where "knights" are replaced by gunslingers. Most of the wonders of the past are seen in a negative light depicted as the cause of the old one's hubristic downfall. Most technological items are seen as cursed. In particular people think that an ancient malevolent god of fire and furious light known by many names such as "conoco, exxon, texaco, and shell" ruled over people. He demanded his followers drive fiery chariots at ludicrous speed into each other. When his crazed worshipers weren't doing this they were on endless pilgrimages to all of the various holy sites where they fed their beastly chariots of noise and fire with holy water of light from sacred mechanical fountains, and purchased dark religious totems and ointments for their hateful machines from the gleaming chrome and glass temples bearing their dark lord's many names.
Why not have people from your new society view petroleum combustion engines as a source of great evil that harmed the planet and led to greedy violent wars that almost destroyed humanity? To them crude oil is a black physical embodiment of evil and greed that must be handled sparingly with extreme care, and that's when the nasty stuff can even be found and collected in the first place.
A lack of readily available oil (we have used up most of the easy-to-get-to oil) made the internal combustion engine a poorer competitor to whatever the alternative is. (This might be easier to answer with more than vague handwaving if you specified what they used instead of cars.)
They use boats instead.
In your future, it is wet. Too wet for roads or rails. Travel is by boat or by air. Instead of roads they have waterways and canals.
Assumptions - please confirm these in the question:
The setting for this question is Earth or an Earth-like world 1500 years after some apocalypse.
A human civilisation has attained a general level of technology comparable to the early 20th century or later.
There is no question that wheeled transport will be in use from day 1 of the apocalypse, even if motive power is provided by human or animal muscles. So the question is why with increasing technology an engine isn't used to replace the muscles. Several options:
The horse breeders possess massive political influence. They outlaw powered vehicles except on dedicated routes - so railways are viable but not cars and trucks. This may be reinforced by a scare campaign based on historical records of the carnage on roads. (They may be donkeys or moose or huskies rather than horses, but the principle remains the same.)
As @ Mark Olson answered, the lack of accessible oil makes it harder to develop a compact engine, limiting self-propelled vehicles to railway engines. This results in infrastructure development focussing on mass-transit railways for both long distance and internal city travel. By the time cars are possible, the cities don't have the road structure to support them as a viable alternative, all travel is planned around rail transport, cable cars, trams etc.
The government wants to keep control of where people go. Automobiles and motorbikes are symbols of freedom, as they allow people to go where they will either alone or with a few companions. An authoritarian government with knowledge of its history will nip this in the bud by hindering their development, or ensuring that only large cargo-carrying vehicles are developed and keeping a tight control on the infrastructure for refuelling points. Which leads to the next point...
Population numbers are insufficient to develop the infrastructure needed to support automobiles. It is taken for granted today, but it requires massive spending to develop and maintain the network of roads, fuel distribution points and vehicles that exist. Scale efficiencies let this work (very profitably) in our society, but for a scattered, poor society (there must be a reason why they've taken 1500 years to regain the technology base) it may not be possible to attract the initial investment.
An ancient airplane is found amongst the ruins. Against all odds it still works! One man learns how to fly it and he is hailed as a god! A religion forms around the flying machine and the future is set!
"All hail the air plane! It brings you closer to god!" Why would you ever want to stay on the ground in a dumb old car when you can soar in the sky, where god is! A plane can get to wherever you're going faster anyway! May god and the Wright Brothers bless you!