Just as you can be wildly off in your estimate of how much you slept during a night you can be wildly off in your estimation of your own alertness and mental state. You can be wrong about how you feel, for much the same reason placebos work or people are suggestible; we don’t actually have a privileged window into our own minds, we’re observers too.
I agree. I've tried to keep a detailed log of my sleep, including how I felt next morning and throughout the day and to my frustration I never figured out how to even remotely reliable measure sleep/rest.
Is sleeping 8 hours better than sleeping 4 hours? Depends...