Both Young and Cohen may have been influenced by the brief appearance of the term in Marshall McLuhan’s 1964 book Understanding Media.

Evidence

See also Young, 1971: Marshall McLuhan, moral panics and moral … (SAGE Journals)

corroborated: 2 independent passages support this claim
XREF: connects to: Folktales can escalate into moral panics in troubled times. — Lynley Hood, A City Possessed, 77; Stanley Cohen showed how a small event can grow into a national moral crisis through media exaggeration, public fear, and official control measures. — Moral Panic; The phrase ‘moral panic’ was first used by Jock Young in 1971, but Cohen notes inspiration from Marshall McLuhan’s work on media. — Moral Panic: A Concept Adrift — University Ethics Observatory

The phrase ‘moral panic’ was first used by Jock Young in 1971, but Cohen notes inspiration from Marshall McLuhan’s work on media. (similarity 0.90)
First coined by Jock Young (1971) and, later, Stanley Cohen (1972) (similarity 0.87)
The term ‘moral panic’ experienced a significant rise in media usage. (similarity 0.84)
Stanley Cohen showed how a small event can grow into a national moral crisis through media exaggeration, public fear, and official control measures. (similarity 0.80)
The term was coined by Stanley Cohen in his 1973 book Folk Devils and Moral Panics. (similarity 0.79)
Cohen (1972, p. 9) defined moral panic as a condition where a group emerges to become defined as a threat to societal values and interests, presented in a stylized way by mass media. (similarity 0.78)