He does. Things like recoil are never really shown in the anime in Gen III or earlier, but are shown from Gen IV onwards. Check out Ash's final battle with Paul if you want to see this in action. I haven't watched that in a long time, so my memory might be wrong, but I'm pretty sure you see things like this in it.
Pikachu runs at the opponent. Its body then becomes surrounded by golden electricity, and it tackles the opponent. While covered in electricity, Pikachu's body looks black and white. When hit by recoil damage, its body becomes surrounded by yellow sparks of electricity.
So he does show recoil damage later on.