Clicking "use" on an item should make the inventory UI disappear, and again re-appear on activating the "use" function with another object.

This could be only certain items, such as fish, where they need to be used on external objects to activate a function.

Items such as logs should never de-activate the inventory window.

Another option is to make the opacity of the inventory window very low when an item "use" function is called, around 30%, and allow click-through. Or, you could whip up a custom UI button that pops up saying "on another item," which will bring back the Inventory UI once the "use" function has been called.