The 31-year-old former Arsenal goalkeeper agreed a new deal on Friday which keeps him at Underhill until 2016.
Stack joined the Bees in the summer on a free transfer and recently captained the side in the absence of player/coach Edgar Davids through injury.
Barnet may be embroiled in a relegation battle this season but Stack is hoping for brighter things in the future.
He told the club's official website: "I want to be successful and hope the club can achieve promotion during my time here because I want to be a Barnet player who is remembered for achieving something.
"This season has been a tough one but we have shown during the past month that we are capable of beating anyone. There is a way to go but we have big aspirations.
"I was delighted to be made club captain. It was an absolute privilege and I am very proud to have led the team.
"I believe I have good leadership qualities and cope with the responsibility well. I have always played and led that way with or without the armband."