Summarize this article:

The extend to which you extend it will depend on how dramatic you want your sad pout to look. Be aware that it will come off looking fake (and not as attractive) if you overdo it.  You should feel your chin wrinkle slightly as you do this. Your mouth should be closed for a sad pout, unlike for a seductive pout. If you're able to, you may want to quiver your lower lip, which will make you look like you're about to cry. This shows that you are feeling vulnerable or submissive. Make eye contact with the person you are talking to, but don't raise your head. Your eyes should be peering up at him. The more eye contact you make, the more flirtatious you will appear, so be cautious is you want to look genuinely sad. If you're trying to be sad in a flirtatious or playful way, you can bat your eyelashes. Don't do this if you want to look genuinely sad. When you are sad, you can see the emotion in your whole body, not just your face. Try slouching your shoulders a little and loosely crossing your arms in front of you. This will let the other person know that you are hurt and trying to protect yourself. You may also consider fidgeting or nervously moving your hands. To sound sad, try talking in very quiet voice and a monotonous tone. Keep your sentences short and to the point. To take your sad voice a step further, try to make your voice tremble, as if you're fighting back tears.

Summary:
Stick your bottom lip out. Drop your head slightly. Get the eyes right. Use your whole body. Master a sad voice.