Pope has enjoyed an impressive season for the promotion chasers, scoring 27 goals in all competitions, including 25 in 39 league appearances.
Veteran Exeter forward Cureton was up for the award after scoring 20 goals, while midfielder Jones has been an influential figure for Bradford City since joining from Rochdale last summer.
Bradford did pick up one honour, however, as boss Phil Parkinson was recognised with the Outstanding Managerial Achievement award after leading the club to the Capital One Cup final.
The League Two side knocked out Wigan Athletic, Arsenal and Aston Villa before losing 5-0 to Swansea City at Wembley last month.
The Apprentice of the Year award went the way of Barnet striker George Sykes, who has made three substitute appearances this season.
Sykes came out on top from a three-man short list which also included Jamie Allen of Rochdale and Plymouth Argyle's Tyler Harvey.
The Credit To The Game award, which recognises the contribution of a player who has retired in the past 12 months, was given to current Fleetwood Town manager Graham Alexander.
The 41-year-old retired at the end of last season after a second spell at Preston North End, and he also played for Scunthorpe United, Luton Town and Burnley during a distinguished playing career.
Alexander also collected 40 caps for Scotland and was appointed as manager of Football League newcomers Fleetwood in December.
Exeter provided the Fan of the Year after Neil Le Milliere was named the winner.