Killing a cockroach naturally may not cause it pain, but rather provoke an avoidance reaction. Pain is a highly subjective experience involving emotional and psychological responses, therefore the relatively simple organization of insect central nervous system is unable to allow the cockroach to consciously experience pain.
If you killed a cockroach through natural means such as soapy water or a mixture of borax and powdered sugar, it might retreat from the harmful stimuli or writhe in an appearance of pain. However, responding to painful stimuli and experiencing pain are different. C.H. Eisemann suggests that if insects felt pain, they would show protective behaviors of injuries, such as limping on a damaged leg.