Curci lead the University of Tampa Spartans to a 25–6 record in three seasons (1968–1970). After his team defeated the Miami Hurricanes at the Orange Bowl in 1970, and Tampa finished that season 10–1, he was hired by the University of Miami. Curci's tenure as Kentucky's coach ended after 9 seasons, longest of any Kentucky coach. In his final game as Kentucky's coach, Curci led the Wildcats to a 21–10 victory over Tennessee on November 21, 1981. Curci later coached in arena football with the Tampa Bay Storm in 1991 and did radio broadcasts for Tampa Bay Buccaneers and college football games.