Actually as the question uses throttle its easy to explain you need to increase.
The same theory holds that the thrust must be the same.
The throttle needs to be opened up because the power output of the engine is related to the amount of fuel burned so as you get higher the density drops off which means for the same setting of the throttle fewer oxygen molecules get in so less fuel is burn so you are not maintaining thrust.
So the only way to get the same mass of fuel burn't is to get back to the same amount of oxygen molecules as you had before. Because the density has dropped you have a larger volume through and the only way to do that is to advance the throttle.