There is absolutely no need to feel embarrassed because you cannot do a full pushup. For the ladies, men naturally tend to have more upper body strength and so it might take you a while to build any strength there at all. For the gentlemen, you still need to practice to be able to do anything so don't feel like you've got it.
If you cannot do a pushup, where do you start?
Try it on your knees: People always say these are girly pushups, but guess what? Those who do it are working their arms as well, even if it is less than doing a full pushup. You may need to start here and build your strength and posture before you can get a full one.
Make sure your posture is right: I have seen all kinds of pushups from butts sticking out to butts sagging low to palms all the way in front of you. When doing a full pushup, your body should be straight (sometimes that hot booty can't be completely straight), and your palms should be in line with your shoulders; they can be wider than the shoulders, but they should be at the shoulder level.
Do other upper body strength exercises: Lift weights, do some downward dogs, etc. but do whatever would get you to build that upper body and core strength so that as you keep trying with the pushups, one day it would happen.
Build up core strength with planks: Your core does a lot of the work with pushups. So as you are building up the strength to do one, start with planks to build that core strength. Maybe start with a 10 second plank, and go higher and higher from there. As your plank time increases, your core strength is increasing as well.
Cheers Eights Weights!