Dempsey, who signed a contract extension in February after being linked with moves to Burnley and Barnsley, was handed the skipper’s armband by boss Keith Curle for the home win against Cheltenham in March.
The 19-year-old also captained the Cumbrians in their home draw against Hartlepool on the final day before winning a clean sweep of player of the year awards at the club’s annual dinner the following night.
Dempsey, a scholarship player with rugby league side Wigan until the age of 16, told the club’s official website: “It was great to get the armband again for the last game of the season in front of such a big crowd.
“I don’t know if I’ll get it again next season but it’s something I would like to do if the gaffer thinks he can show that kind of faith in me.”
Midfielder Dempsey was the Cumbrians’ top scorer this season with 11 goals from 47 appearances. He made his first-team debut in January last year and a further three appearances at the end of the last campaign.
“I’ve been really motivated since I was a kid,” he added. “I’ll never settle for second place so all I’ll be thinking about over the summer is coming back and being first at everything I do.
“It’s all about being ready for the first game of the season.
“I’ve seen the gaffer say he wants me to get to 20 goals, and the only way to do that is to be out on the pitch as much as possible.
“If I could do that it would be absolutely massive for me.”