Wake-up grogginess is a universal thing for any being with a brain. Even insects (probably).
However most animals have more natural sleeping patterns which includes a whole lot of light napping which won't cause drowsiness in the same degree. That's how a dog can also go right from sleeping to barking out the window in less than a second, when it's only sleeping lightly.
So, when we are amused by a sleep-drunken dog, it's because it reminds us of the result of our own socially adapted and unnatural sleep cycle and relate it to our own sick experience.
Drowsiness from sleeping can also be a sign of dehydration, so make sure to to get enough water for you and your best friend.
(I just googled it for less than a minute, so I'm an expert now.