You can't it is a natural part of the decomposition of the wood.

You'd have to change the material you've used to build the wood from fallen trees to pressure treated timber. The fallen trees are rotting, and toadstools/mushrooms help to do that work.

The mushrooms will normally do no harm to your plants and there is nothing much you can do about them. There is only one really that you don't want at any price in the garden as it will attack some trees and shrubs, and that is the honey fungus, armillaria mellea. It is quite a large one, yellow and rather scaly on both cap and stem. In the soil it makes a network of black threads rather like bootlaces, and if you get that one best ask for advice!