Power effeciency of Zener diode regulator
I gather you're not impressed by 16mW to the load while taking 3 watts from the battery? Yes, efficiency is Pout/Pin.

Shunt regulators are not used for efficiency, they are used for their simplicity. 

Most people wouldn't use such a low value resistor as R1 for that load. How did you choose the value? Think about what the constraints are on the value of R1.

Use a three terminal series pass regulator if you want to waste less power. With a 4v load, and a 12v source, an ideal 3 terminal regulator would not exceed 33% efficiency.

To approach 100%, you would need a switching regulator.