Jones was named on a three-man short-list alongside Exeter striker Jamie Cureton and Port Vale forward Tom Pope, who won the individual League Two prize at the weekend gala at The Brewery in London.
"If you keep yourself fit and you've got desire, and if you are lucky with injuries, you can play a lot longer these days," said Parkinson, who won the Outstanding Managerial Achievement award for guiding his side to the Capital One Cup final at Wembley.
"Look at Ryan Giggs and Gary is an example of that. He's an outstanding captain.
"We've only had him a year, but he's an inspiration on and off the pitch. To be in the top three is a great accolade for him."
Jones, who started out at Swansea in 1997 before spending most of his 16-year career at Rochdale, joined Bradford on a free transfer last summer and has already made 44 appearances for the Bantams this season.