Feeling tired has absolutely nothing to do with sleep deprivation.
I can (and do) stay up for 72 hours feeling as wide awake & fresh as if I'd been sleeping 7 hours a night, every night, for years. My old work had to train us to both
use that,
and to account for it. Because after 24 hours? No matter how wide awake / not sleepy you feel? Your judgement and reactions will start to be impaired. Longer you're awake? The more impaired you're gonna be. Learning to operate in sleep dep is like learning to handle your drinking. Just because you're used to drinking? Doesn't mean you're not double the legal limit, or that your judgement and reactions aren't impaired. Your simply used to functioning while altered.
Another way to think of it is that anxiety produces chemicals that are what Meth & Coke & other stimulants
replicate. New parents and other people who don't have the anxiety component, or emergency component, or drugs simulating/stimulated feel
exhausted by sleep dep, more often than not. Chronic insomniacs, people suffering from anxiety, military & other emergency workers, drug users? They don't generally feel tired... Until the chemicals keeping their brain awake-awake-awake... wear off. Or they're so chronically sleep deprived that how tired they feel is now meaningless. Tired numbs out along with every other feeling.
Here's some plain English reading :)
http://www.livescience.com/52592-spooky-effects-sleep-deprivation.html
A single good nights sleep? Will do wonders. But you still won't be functioning 100% until you're getting regular sleep... For awhile. I forget the actual numbers. But I think it was something like 3-10 days, on average? But could run as much as several weeks to a few months for chronic conditions? Something like that.