Second half goals from Cheye Alexander and Jack Barham secured three points and secured a 13th place finish with 60 points.
Alfie Rutherford had the first chance nine minutes in, but his downward header went wide of the post.
Jack Barham knocked the ball down for Shaq Coulthirst shortly afterwards but his effort from the edge of the box was blocked.
The Bees top scorer did find the back of the net, however the assistant referee’s flag was up for offside.
Havant keeper Bilboe produced a good save to deny Jack Taylor and Coulthirst before a lucky escape at the other end.
Mark Cousins lost control of the ball 6 yards from his goal, Fogden squared to Rutherford who had an open goal but was denied by an unbelievable block from skipper Callum Reynolds.
Barnet took the lead after a bright start to the second half.
Coulthirst had a shot deflected, it struck the arm of a defender but dropped to Cheye Alexander who fired it through the legs of Bilboe and home.
The Bees were again denied by the offside flag soon after a wonderful ball over the top from Jack Taylor was lobbed over the keeper by Simeon Akinola, but he strayed slightly offside.
Substitute Akinola had another chance soon after after Boucaud led a break away, but again Bilboe saved.
Barnet made it two following a great move. Akinola fired at goal, it was deflected and going wide but Jack Barham was alive to it and did well to prod it home!
Rutherford fired across the face of goal in a rare Havant chance before Mason-Clark powered a shot wide of the left post from a corner.
Substitute Mason-Clark soon forced a save which was parried by Bilboe but Akinola couldn’t turn the rebound home.
Another reinforcement was causing issues for the home defence, Antonis Vasiliou beat his man to make half a yard of space, fizzed the ball across goal but no-one managed to get a toe on the end of it.
Jordan Rose’s spectacular scorpion kick tested the gloves of Cousins before Vasiliou teed up Jack Taylor who was again denied by the home keeper.
Barnet – Cousins, Alexander, Johnson, Reynolds, Robson, Coulthirst (Akinola), J. Taylor, H. Taylor, Boucaud (Mason-Clark), Tutonda, Barham (Vasiliou)
Unused- Matrevics, Box
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