A common word which means the opposite or inverse of what is expected is contrary. It's often used in phrases like "on the contrary" or "to the contrary" when talking about the direct opposite of a desired effect.
Similar words include contradictory and antithetical. Contradictory tends to have connotations of evidence or information, as in contradictory statements, and antithetical is more often associated with beliefs or principles than expectations or outcomes. Contrary is more likely to be associated with an outcome or result.
"I expected gas prices to rise on the announcement of the embargo, but quite the contrary, they actually dropped."
It could be used in the example sentence like so...
"I got 8 hours of sleep but I'm more tired than when I went to sleep. That's so contrary."
and this would be understandable by most people, but would sound archaic or off. It would more commonly used in a phrase like "contrary to expectation."
A more likely example would be something like this:
"I got 8 hours of sleep, but I don't feel rested. On the contrary, I feel more tired than when I went to sleep."