Think in English a bit. Would you sleep a car? Not really, right? The verb is intransitive, you don't need a direct object. And if you really want to use one, you'd say what you slept - a nap, a beauty sleep, etc.
German "schlafen" is the same deal, it requires no direct object. And if you were to force one, you'd end with something like "ich schlafe meinen Schönheitsschlaf" (I sleep my beauty sleep) - note how the accusative is there.
So the role of that "in meinem Auto" (in my car) is something else: it's an optional complement telling you where that action happens. German typically handles this through prepositional phrases (Präpositionalphrase), so the preposition dictates which case you need to use:
- some ask for the dative; e.g. "mit" (with), "bei" (by), "von" (from)...
- some ask for accusative; e.g. "für" (for), "gegen" (against), "ohne" (without)...
- some allow either; e.g. "über" (over), "neben" (near), "in" (in).
When the preposition allows either, typically you use the accusative when the subject is changing locations. For example:
- ich laufe in den Wald (I run towards the woods; like, I'm running and I reach the woods)
- ich laufe im [=in+dem] Wald (I run in the woods; like, I'm just jogging there)