The spell sends creatures into a magical slumber. […] each creature affected by the spell falls unconscious until the spell ends, the sleeper takes damage, or someone uses an action to shake or slap the sleeper awake.
The spell makes it clear that it puts the creature to sleep. Note the many reference to sleep sleeping and awake in the spell effect description. The unconscious condition is simply a mechanical way the game models sleep, but it does not change the fact that the spell indeed puts a creature to sleep.
The Aspect of the Moon invocation says:
You no longer need to sleep and can’t be forced to sleep by any means.
Having this aspect clearly then negates any attempt to put the warlock to sleep. And since sleep tries to do just that, the invocation allows them to be completely unaffected by the spell.