Antidepressants are not narcotics. Legally a "narcotic" is either an opioid like heroin or morphine or it is cocaine/crack. Medically the term "narcotic" only refers to opioid analgesics. Most doctors and scientists do not like using the word narcotic because most people do not understand exactly what a narcotic is. An antidepressant is not a narcotic nor is it a drug of abuse. Antidepressants are not controlled substances and drug seeking behaviour has not been scene in people taking antidepressants.
It can be argued that amphetamines in particular might be considered narcotics as they are occasionally used in people with severe refractory depression. However technically amphetamines are not narcotics.