The Bees battled hard but came away from the game disappointed after only drawing with Boreham Wood.
Shaq Coulthirst had the first effort of the game two minutes in, but his effort was claimed by Huddart.
Justin Shaibu forced his way into the box before delivering a cross that was cleared behind. Tom Champion headed over the following corner.
The Bees were attacking well and Ephron Mason-Clark was enjoying himself out wide, causing plenty of issues for the Boreham Wood defence.
Jack Taylor fired over the bar, as did Coulthirst midway through the first half.
Ricky Shakes had a powerful effort at goal held by Mark Cousins before Charlee Adams shot high over the bar.
Skipper Callum Reynolds had to be replaced shortly after the restart, coming off worse for wear following a clash of heads.
His replacement Simeon Akinola almost gave Barnet the lead, but he came up just short on the slide attempting to poke home Mason-Clark's through ball.
Mason-Clark then had an effort palmed away by Huddart before there were big appeals for a Barnet penalty waved away after Akinola's shot appeared to strike the arms of Champion.
Moments later, Boreham Wood were lucky not to be reduced to 10-men after a reckless challenge from Kieran Murtagh was only given a yellow card.
Barnet took the lead in the 68th minute thanks to a wonder strike from Ephron Mason-Clark.
The 19-year-old cut inside to shoot on his left foot from the edge of the box and fired it high into the top left corner.
Huddart then produced a great save to deny Taylor from doubling the lead
Boreham Wood were given an opportunity to tie the game after being awarded a controversial penalty late on following a foul by Akinola.
Bradley Ash stepped up and calmly slotted it home, sending Mark Cousins the wrong way in the process.
Barnet - Cousins, Alexander, Johnson, Reynolds (Akinola 52), Robson, Adams, Coulthirst, J. Taylor, Elito, Sweeney, Mason-Clark (Harrison 87)
Unused - Matrevics, Fonguck, Tutonda
Attendance - 2,087 (305 Boreham Wood)