I've been using a the same method for years with great success. I found a roll of plastic mesh at a garage sale many years ago--my husband says it's used for keeping leaves out of gutters on the house. I cut it to fit whatever area I want to protect and simply lay it over the soil. I've cut metal pins out of old hangers to secure the mesh in place. But I've also just used sturdy bits of twig or even stones to hold it down. I've used it to cover seeds in the flower beds (they love to dig up sunflower seeds!) and on the soil in potted plants outside. Hope this helps, it's worked wonders for me and I always seem to find another roll at a garage sale about the time I need a new one. Though it's not expensive if you have to buy it in a home store.
Squirrels like to dig in soft dirt, so you might try covering the soil with gravel or rocks.
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