After retirement as a player, Curtis became Commercial Manager at Coventry City in 1972, going on to become an executive director at the club and then managing director, in September 1983. In April 1986, with the club facing their third successive relegation battle, and having gone eight games without a win, manager Don Mackay left the club. The board asked Curtis and youth-team coach John Sillett to take charge for the final three games. Coventry won two of those three, and escaped relegation. The pair remained in charge for the 1986–87 season; officially Curtis was the manager, while Sillett was first-team coach, but the two were effectively joint managers. The team achieved a 10th-place finish that season, while also winning the 1986–87 FA Cup, which is the only major trophy Coventry have won. The cup run began with a home win over Bolton Wanderers, followed by away victories over Manchester United, Stoke City and Sheffield Wednesday, with the semi-final being a 3–2 win over Leeds United at the neutral venue Hillsborough. Prior to the Manchester United game, in January 1987, Curtis told reporters that "our name is on the cup". In a match regarded by many pundits as one of the greatest finals in the history of the competition, Coventry beat Tottenham Hotspur 3–2 in the 1987 FA Cup Final at Wembley Stadium.