Revive St. Augustine grass?

Long story short: I intended to kill sprouting weeds in my yard with one of those "kills-the-weeds-not-the-lawn" products purchased from Home Depot. About a week ago (one week after application), my lawn developed multiple browning spots. As a novice, it looks like some of these spots are complete dead patches.

I think this likely resulted from user error. I didn't do much research and probably applied a product not suitable for St. Augustine grass. But the mistake is behind me now.

I would appreciate any recommendations on the best way to revive this grass (if possible) without laying new sod.