The economy is a complex system, the only way to be sure that when you change something somewhere the energy consumption will remain constant is to put a constraint on it. You could set quotas, increase/decrese taxes to drive it to the desired targets, etc.

Imagine the system is at equilibrium at a certain output and energy usage and you discover a device than increases efficiency in the use of energy by 10%. The system could produce the same output as before using 10% less energy. But the new equilibrium won't be the same output at 10% less energy consumption, because some resources will be freed in the energy generation sector and the price of energy will go down resulting in some activities that were not economically viable before becoming viable. Maybe desalting sea water was too expensive before, but with lower energy prices and higher efficiency it does make sense, for example. You will have an increase in output but whether the new energy consumption is below or above the original level depends on the details. The latter is more likely, I guess.