The best solution is for these windfall apples to never exist in the first place. Most apple varieties fall into a biennial bearing pattern. They produce a very heavy fruit set in year N. The burden of bringing this large quantity of fruit to maturity suppresses fruit bud growth (which happens in the fall). In year N+1 there are negligible fruit buds and so little or no fruit is set. This leaves all the tree's resources to create fruit buds in the fall and in year N+2 you again have an extremely heavy fruiting year. Most apple varieties will set such heavy fruit in year N, N+2, etc that they cannot bring it all to maturity. This contributes to windfalls, "june drop", as well as under-mature fruit at the end of the season.
Instead of allowing the tree to fall into this pattern, thin the fruit set before fruitlets reach the size of a US quarter. Note that whatever fruit is set you will have to eventually handle (if you are planning to clean up after the tree). You can handle it when it is small and on the tree or you can clean it up off the ground. If you thin it from the tree, you will have less material to deal with (by composting or otherwise) because you will be taking smaller fruit off the tree before it can grow and fall. Correspondingly, by taking fruitlets off when they are small, you are allowing the tree to direct its resources towards the remaining fruit. This means more fruit will reach maturity and those that do will be larger, healthier, and typically sweeter. You can also be selective in your thinning - take fruitlets that already have insect damage, fungal damage, or are incompletely formed. This further improves your eventual harvest by increasing the number and proportion of well-formed, undamaged fruit the tree eventually brings to maturity. Finally, by thinning to a manageable number of fruit you leave the tree with energy to create fruit buds for the following season, giving you more even production from year to year.
Even if you thin, you will still have some drops. These, along with the thinnings, should be removed from the area. If you compost them, compost them away from the tree. Fungus is a healthy and essential part of the composting process but you do not want to encourage fungus that eats apple biomass to grow beneath your apple trees. If you do, you may find it moves from your drops to the tree itself, damaging fruit you left on the tree for eventual harvest or damaging foliage or even branches of the tree itself. Take your compostable material as far from your apple trees as practical and let the fungus go to work there.
Citation: The Apple Grower: A Guide for the Organic Orchardist. Michael Phillips.