David wrote the Psalms--probably all of them (those which claim the name of later kings and times were probably written prophetically). Augustine has already exposited one Psalm, and could very well do the rest to continue to prove his point. The problem is, in order not to be accused of selective proof-texting, he would have to exposit all of each Psalm, and that would take a lot of work. So instead he encourages us to take up his writings on the Psalms.
Yet, despite his claims not to have time to discuss in detail, Augustine proceeds to show how specific Psalms point to the church in their intermingling of literal and figurative language.