Some cultivars of St. Augustine are considerably more shade tolerant than others. Your options depend on how far north you are in the state.

Monkey/Mondo grass has been the best heavy shade low grass-like option for us. A little slow to fill in, but pretty rugged if kept out of full sun during the hottest time of the year.

My mother grew Pachysandra in small beds/plots flanking her front door in Texarkana and just love it. It's hardy, filled in quickly after they built their house, and was gorgeous 15 years later when they sold the house. I've never grown it myself, but I always liked hers. It LOVES shady spots but her two beds got some sun also, it will tolerate some sun. Here's a video of some plantings of it. I understand it spreads by roots and not wind-blown seed but Mom' never got out of control along her sidewalk approach. https://www.youtube.com/watch?v=e_1hKB9-NGg 

I second mondo grass, but also Big Blue Lirope.

Ajuga is good for shade. Berkley sedge and Meadow sedge do well on my limestone hills. Many people are using sedges as a no mow grass.

Various Sedges

Salvia roemeriana seeds out and gets a good ground cover given time.