There is no need to kill every single zombie on a level, it is more benficial to reserve your ammunition for when you really need it. Each level contains loot crates which will replenish your ammunition, they are signified by a green flare and are collected automatically when you run over them.
There is no way that you can reload your weapon manually so it is important that you pay attention to your ammo depletion as being left without ammo will leave your character vulnerable. If you do find yourself low on ammunition try to find large gaps between zombies and steer your character towards these so you can get past the zombies without having to use ammunition.