In Michtav M'Eliyahu vol2. page 137 Rabbi Dessler explains that the primordial snake was an external manifestation of the evil inclination which entered man after the sin.
If so, why was the snake punished if it was just doing its job of enticing man which is what it was created for? (as written in Gen.3:14: "And the Lord God said to the serpent, "Because you have done this, cursed be you more than all the cattle and more than all the beasts of the field; you shall walk on your belly, and you shall eat dust all the days of your life.")