Carnevale graduated from Somerville High School in Somerville, New Jersey. He then played for the fabled Howard Cann at New York University. He was a member of the 1935 NYU squad that was named national champions by the Helms Foundation. He played in the first National Invitation Tournament (NIT) in Madison Square Garden in 1938.
Carnevale served in the Navy during World War II as a gunnery officer and was torpedoed in December, 1942, spending several days in an open lifeboat before being rescued. He received the Purple Heart.
He coached at the University of North Carolina (1944-46) and the Naval Academy (1947-67). In 1946 he guided his Tar Heels to the NCAA championship game, where they succumbed to Oklahoma A&M (coached by Hank Iba and led by 7-footer Bob Kurland).
He compiled a 51-11 record at Carolina and a 257-160 record at Navy, despite the Naval Academy height restrictions (no students taller than 6'4" were admitted). He then served as Athletic Director at his alma mater, NYU, (1968-72) and at William & Mary.