There are products labeled for use on St. Augustine. However I find that they are marginally effective or can actually damage the St. Augustine if used at certain times of the year.
I use a weed wiper that I build homemade and apply glyphosate (Roundup is one brand) at a strength of 5%. With the wiper and some care I can get the product on the nutsedge but not on the St. Augustine. A little "oops" damage is acceptable to me if I am to get rid of weeds but I find that with care I really don't get much "oops" damage! The best time to do your weed wiping is in spring to summer but you just need to stay with it for a season or two as there will be some resprouting and some tubers that were dormant may sprout later on. Whenever the nutsedge is growing it needs to be treated.
The following web site shows how I build the weed wiper:
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