The Bantams passed up several decent openings in front of goal as the hosts proved far more clinical as they scored twice through Taiwo Atieno and John Oster with merely their first two chances.
City huffed and puffed for most of the second half but ultimately they had left themselves with too much of an uphill battle to face.
James Hanson went close early on when he fired wide from just inside the area after being picked out in space by an angled pass from Ritchie Jones.
Barnet's key man Ricky Holmes went close to scoring himself shortly after; John Oster played a short corner to Barry Fuller who whipped a cross into the area that was glanced wide by Holmes.
The chances kept coming in a frantic opening to he first half and after Will Atkinson had squared the ball to Gary Jones, the latter proceeded to hammer a rising shot over the bar from 20 yards out.
Coming up to the half hour mark, City almost went ahead through the unlikely source of Stephen Darby; James Hanson's flick from Nathan Doyle's throw came all the way across to Darby who fizzed a powerful half-volley over the bar.
Gary Jones tried his luck once more soon after with another strike from distance, his half-volley this time was on target but it was well watched and held by Graham Stack in Barnet's goal.
James Hanson dispossessed giant centre half Andrew Iro before squaring the ball to Nahki Wells who fired a shot over the bar on the turn.
Despite all the early attempts on goal coming from the visitors it was Barnet that went ahead before the interval; Ritchie Jones was caught napping deep in his own half and he was dispossessed by Elliot Johnson who fizzed a cross into the area that was bundled home by former Torquay frontman Taiwo Atieno.
City went close early in the second half when Wells swept a shot wide when Hanson had found him after beating Iro to a Ricky Ravenhill pass, but it was Barnet who scored next.
Rory McArdle did well to win possession but he instantly ran into traffic and was robbed by Ricky Holmes who fed the ball to John Oster in space, he composed himself well to fire past Matt Duke and double his side's advantage.
Stephen Darby found Nahki Wells with a neat pass and his shot was deflected across the area and almost scrambled in by Gary Jones, the ball then came back to Wells who struck a firm half volley wide of the target.
Ricky Holmes, one of Barnet's most impressive performers, then forced a smart save from Matt Duke; after cutting inside from the left hand side he produced a powerful shot that Duke had to push wide.
The Bantams thought they had a goal back when Kyel Reid's early cross was headed in neatly by James Hanson but the flag went up for an offside against Hanson as he peeled away from his marker.
Kyel Reid's crosses were causing problems in Barnet's area and one of his deliveries was headed towards his own goal by Andrew Iro but as it looked to be heading past Graham Stack he was rescued by a teammate who headed the ball clear from under the crossbar.
Gary Jones hadn't given up trying to beat Stack and his freekick dipped over the wall but he couldn't get the shot on target as it dropped a yard or so wide of the mark.
City thought they should've been awarded a penalty when James Hanson was shoved in the area by one of Barnet's towering centre halves but the ref waved it away and the ball came to Alan Connell who thumped a shot over the bar from inside the area.
Nahki Wells tried his luck with a couple of efforts in injury time; the first he dragged wide after finding a yard of space on Stephens and the second was a shot that he fired into the side netting after Iro had failed to deal with Matt Duke' long punt. This, though, was the last of the action as The Bantams suffered a miserable defeat in North London to somewhat sum up their luck in front of goal during the 90 minutes.