Groggy
/ˈɡrɑːɡi/
Definition 1 of 2
Pro Tip 1/3Not just tired
Groggy implies a struggle with both mental and physical activities, not just feeling sleepy. 
I tried to answer emails, but I was too groggy to focus.
Pro Tip 2/3Temporary state
Groggy is used for a temporary condition, often just after waking up or during illness. 
She was groggy every morning until her first cup of coffee.
Pro Tip 3/3Recovery period
Use 'groggy' for the time when someone is recovering from being knocked out or anesthetized. 
He was still groggy after the anesthesia wore off.