You don't feel it goign to sleep, only when you move it again and get the 'feeling' back in your limbs. You cut off circulation to your body part, and no oxygen rich blood can get there. Your cells start to die. When you move and the blood flows back in, it's basically bringing them back up to speed.
It's why heart attacks are so bad, the heart stops pumping and no fresh blood +oxygen gets to it, and the tissue starts to die