Poast is a brand name of sethoxydim.You suppose it's a modern replacement for Poast?
Like NH said I have used it to clean up grass in clover, I couldn't find any around me and they wanted to sell me some Poast for $180/2gal and that's the smallest they had, talked to Mo and he had some to me for about $65 including shipping.
As stu said, grasses are hard to control long term with only mowing. This is mainly due to the fact that many grasses that wouldn't produce a seed head until they reached a certain height, will start to produce them at an ever lower height the more you mow them, eventually producing viable seed when only 4"-6" tall. The other problem with only mowing is that certain types of grass, like crabgrass for instance, have a low, prostrate spreading growth habit that will leave much of the plant intact with all but the lowest mowing heights. You will leave a basically mature grass plant with cutting injury that will try to produce seed heads within days after they are cut.^^^Mowing grass just encourages more of it to spread. Broadleaf weeds can oftentimes be dealt with effectively via mowing, but not grasses IME