It was the Bees who had the better start, Dan Sparkes’ dangerous cross two minutes in was headed away by Carl Piergianni and his header struck Shaq Coulthirst, but the forward couldn’t get a shot away before the Salford defender hooked clear.
A flowing Barnet move saw Dave Tarpey feed the ball to Sparkes who had a goalbound effort blocked.
Tom Walker lined up a shot from the edge of the box but his curling strike was saved by Mark Cousins at the second attempt.
Mani Dieseruvwe fires at goal from 18 yards out but his effort not only cleared the bar but cleared the roof of the stadium.
Sparkes turned provider when he clipped a ball over the top of the Salford defence to Coulthirst but his first-time effort was saved by Chris Neal.
A long throw from Liam Hogan found Devonte Redmond, who curled the ball towards the goal but was denied by the inside of the left post before Gus Mafuta had an effort well blocked by Harry Taylor.
Lois Maynard was the next to strike the woodwork, hitting the crossbar with a low volley on the stretch.
After the break, a fingertip save by Salford’s Neal prevented Shaq Coulthirst from giving Barnet the lead with an edge-of-the-box strike from Taylor’s pass.
Taylor poked the ball goalwards just after the hour mark but his effort was hooked clear by Liam Hogan.
Substitute Rory Gaffney had the ball in the net for Salford in the 70th minute but the referee had blown the whistle for a handball by Dieseruvwe before the striker had put the ball across the line.
Akinola had a header blocked by Piergianni from Elliott Johnson’s good delivery.
The Bees number 14 then chased down a lost cause and managed to keep the ball in play close to the corner flag, he then drove at goal getting past Nathan Pond but shot straight at Neal.
Wes Fonguck was the next to test the Salford keeper, but again Neal was equal to this effort.
The match finished all square at the Peninsular and the Bees earned their third clean sheet in as many matches.
Barnet – Cousins, Alexander, Johnson, Reynolds, Tarpey (Fonguck 68), Coulthirst (Robson 79), Sparkes, Taylor, Boucaud, Sweeney, Mason-Clark (Akinola 53)
Unused – Azaze, Barham.
Attendance – 2,452