If your form is strict on the pushups i.e. you're perfectly straight and your abs are tight so that you're not sagging in the middle, you'll get plenty of ab work there. You'll also get some indirect work during squats as your abs stabilize you. If you feel you're not getting enough ab work then by all means throw in a few sets of planks or reverse crunches or knee ups at the end of your workout.
I know Kevin has already answered in this thread but I'll just add my own two cents about why there's no ab work included in the simplefit program. First, as stated above, you already get indirect ab work in the routine, especially if you're paying attention to form and especially at the higher levels. Second, if you start adding too many exercises to simplefit it ceases to be simplefit and becomes something else. The beauty of simplefit is that it's simple. Beginners of all ages and skill levels can start the program without feeling intimidated by a laundry-list of different exercises, and still see huge benefits, even if they have never exercised before in their lives.