Leaf spot on Swiss chard and beetroot

Hello, I am new to veg gardening and to this site. I planted Swiss chard and beetroot too close together and watered from the top. They both developed brown spots on their leaves which from Googling photos I suspect is cercosporum. I have destroyed all the plants but I would like to know if I have to do anything else to get rid of any residual spores in the soil. I did try a search on this particular topic on this website and couldn’t find anything...any help much appreciated.