No it doesn't, zombies in most things go down when you hit them in a head. And constructs are like machines such as automobiles, there's certainly places that you can hit a car in that will stop it from functioning more than hitting them in other places, like hitting the engine vs hitting the windows.
That zombies go down when hit in the head is a modern concept associated with zombies as disease which does not apply to D&D zombies. And Golems are no construct in the sense that they have different parts like an "engine".