Nah, all you gotta do is damage/destroy the brain. The brain of the zombie is host to the parasitic Solanum virus, and that is what animates them. Destroy the brain, and no more animated zombie.
You might be thinking of those various "Return of the Living Dead" movies, the ones where the zombies are constantly calling out, "Brains! Brains!" Those movies are comedic spoofs, they don't portray real zombie behavior. Real zombies don't eat brains, because if they did, the Solanum virus would be unable to perpetuate itself in new hosts.
For more accurate zombie behavior, watch those "other" zombie movies, the ones directed by George Romero. That guy really knows his zombies.

