Well, unless your feet weight a tonne, it's no surprise that they come up when you try doing crunches on your own. Doesn't matter, though, because crunches don't matter. Almost everyone who speaks English and has come up with some fitness goal has done crunches, but relatively few human beings have ever done crunches in a way that is both safe and productive. Even if you could do them with perfect form, there's still probably better exercises for strengthening the core, if you even need to do core work.
Personally, I haven't had any direct ab work as a key feature in any of my routines since about 2008, yet if you felt my abs they're a lot tougher than the average person's -- this is because you load up the abs in damn near every exercise in the gym. My abs are built on squats, deadlifts, overhead presses and pull ups... you'll never lift 300lb off the ground without bracing your abs.
Your push ups will involve a fair amount of ab work and without knowing what db exercises you're doing, they'll probably be a leading cause of ab development for you. If you need more direct abs work after push ups, then do prone holds and side holds. A prone hold is simply getting into a push up position and holding it, keeping your abs in tight. A side hold is getting onto only one hand/arm and rotating out 90 degrees from a push up position, putting you into a human flag position. Do this on both sides to strengthen up the oblique muscles.