The animals that cannot feel pain are fish.
Fish cannot feel pain as fish lack the essential characteristics and pain receptors like humans have and hence do not feel pain.
And other animals that cannot feel pain are Sessile animals with no brains such as sponges most certainly cannot feel pain.
Jellyfish, also brainless, also can't feel pain.
While fish cannot feel pain the same way that humans and other animals feel the pain the fish can usually feel some irritation.
So when lacking oxygen from being in the water fish can feel a different kind of pain which is more of irritation when the fish suffocates.
So in a way fish do feel some pain but it's not the same pain that humans and other animals feel.
When a fish is removed from the water and exposed to air, its delicate gill filaments collapse, resulting in a greatly reduced surface area for oxygen exchange.
Or when you go fishing and the fish bites into a fish hook.
The fish biting into the fish hook does not feel the pain the same way as humans or dogs, cats etc would feel the pain.
But it is not completely painless to the fish when they get a hook in their mouth.
The fish does feel some form of irritation but it's not as painful as it would be for a human or other animal.