It's probably not clover. It's probably actually Oxalis dillenii or another Oxalis, aka Wood Sorrel or False Shamrock. Clover usually makes pretty flowers. Most of the common Oxalis around here has yellow flowers and burrs.
There's a product that's safe for St. Aug lawns called Weed-B-Gone that should take care of it. It comes in a bag with a spout on it, and you sprinkle the pellets on the ground and then water them in. It's not the best to treat large areas with, though... my recommendation is that you pull most of it up by hand (as it should be starting to mound about now, each mound is usually one or two plants and are easily removed) and then treat if you see it coming back.