The Rocks dominated possession for long periods - but two first-half lapses at the back cost them dear as Concord won this bottom-six battle 2-1 at a chilly Nyewood Lane.
Keaton Wood gave the Rocks hope of a fightback when he got one back with 14 minutes left but despite plenty of late pressure, Bognor could not find an equaliser.
The loss, such a disappointment after a recent run of two wins and two draws, leaves Jack Pearce's team still second from bottom of the National League South table.
They'll need to lift themselves quickly, but their run gets no easier with a visit to Bath City coming next Saturday.
Bognor had so much of the play, they will wonder how they scored only one goal.
It was a clear, dry but cold afternoon for a big game at the bottom of National League South, with Bognor bidding to climb out of the bottom three and go above their visitors with a victory.
The Rocks were without left-back Kristian Campbell, who picked up a minor injury in Tuesday's FA Trophy replay win over Hemel Hempstead. That leaves the club with three left-backs out - with James Crane and Archie Edwards also sidelined.
Calvin Davies switched flanks to the left and Harvey Whyte came in on the right. Injuries to the likes of Ollie Pearce and Corey Heath meant the Rocks could name only three subs. There was a minute's silence before the game in memory of lifelong fan Graeme Bradford, who died last week aged 57.
It was Concord - aka the Beachboys - who were quick out of the blocks, forcing a corner down the left within a minute and scoring within two.
Lewis Taaffe picked the ball up just outside the area, took a couple of touches and fired a low right-foot shot through a crowd of players and beynod Dan Lincoln's dive.
It might have been 1-1 a couple of minutes later as Ben Swallow worked space for a cross from the right that Whyte hooked towards goal only to see it blocked. The clearance hit Whyte and bounced up into keeper Louis Wells' hands. Then Swallow's cross was sliced heavily over his own bar by Concord defender Lewis Knight.
Taaffe's earlier effort had seemingly not been remembered and the Rocks allowed him another shot from similar range - this one floated just wide of Lincoln's right-hand post with the keeper struggling.
Bognor were producing some neat forward play and putting Concord under pressure as they got over the early goal, but couldn't test the keeper within the first 15 minutes - although Ibra Sekajja glanced another Swallow cross just wide. Then the two reversed roles as Sekajja's short pass allowed Swallow room for a drive that Wells got behind.
Wood forced Wells into a fine leaping save when he headed Swallow's cross goalwards on 22 minutes. Concord's Harry Lee was booked for halting Swallow's surge into the opposition half.
Bognor continued to boss things despite being a goal down and a Davies cross from the left was just too high for Jimmy Muitt, who couldn't get enough on his header. Then Tommy Block played an intricate pass into Muitt, whose first-time shot was blocked by a flying defender.
Next Whyte played a teasing ball across the box but Muitt wasn't close enough to stick it in.
From nowhere, and against the run of play, the Rocks were two down. A high ball over the top by Ben Greenhalgh suddenly put Khale Da Costa in on Lincoln and as the keeper came out to the edge of the box, he lifted the ball over him and into the empty goal. That left the Rocks a mountain to climb and the home crowd, understandably, were very quiet.
As they tried a quick reply, Muitt volleyed a Swallow cross well over, leaving manager Jack Pearce shaking his head in the dugout.
The scoreline could have got bleaker for the Rocks on 37 minutes but Greenhalgh's low shot across the goalmouth was just beyond the post. At the other end the Rocks' sixth corner led to an effort being cleared off the line before Doug Tuck sent the follow-up shot over.
At times Bognor were laying siege to the Rangers goal - but they were defending as though their lives depended on it, and were breaking dangerously. Amos Nasha was the second Beachboy to be booked after he tripped Whyte on 44 minutes.
Davies was one of the hosts' most dangerous players but was out of luck as his long-range shot came back off the angle of post and bar with Wells stranded.
The start of the second half again saw plenty of possession for the Rocks but very little in the way of a goal threat. Wood was booked for disputing a decision and there was a scare for the Rocks when a cross from the right bounced across the six-yard box with no-one touching it. The day's second tribute to Graeme Bradford was a minute's applause throughout the 57th minute.
Swallow was the first to threaten a goal back in the second half with a fierce drive along the ground that the keeper tipped away for a corner. Swallow's ball into Muitt saw him go down under the defender's challenge but there was no penalty tp be had - only a goal kick to Concord.
The first substitution of the game came on 71 minutes when El-Abd was replaced by Dan Beck. Concord's Jed Smith was booked with 15 minutes left as Bognor won a free-kick 30 yards from goal - and when the initial delivery was cleared to Whyte, he curled the ball back into the crowded area Wood rose highest to glance a header into the corner of the net.
With Bognor pushing forward, Rangers broke again and a quick attack led to Greenhalgh sending a shot just beyond Lincoln's left-hand post.
Bognor were half-appealing for a penalty with ten to go as Tuck danced into the area and went down - but there was nothing doing. There was a booking for Whyte as he mistimed a tackle to halt a Concord attack down their left wing.
Another Concord booking followed - Jordan Brown cautioned for hauling down Sekajja. Concord brought on Femi Akinwande while Bognor swapped Tommys - bringing on Scutt for Block.
Whyte was named MoM and the Rocks kept pressing, Beck firing a left-footed shot a yard or so wide. Then a scramble in the area fell to Chad Field, who took a touch and volleyed just over.
Concord replaced Greenhalgh with Steve King. As Wells took his time at a goal kick the referee quite rightly booked him for time-wasting.
Tuck ran at the defence and threaded a pass to Sekajja, whose shot on the turn was awkward for the keeper - but he got down to hold on to it. And just as Bognor worked up another attack, the referee ended the game before they'd had a chance to turn it into another effort at goal.
Rocks: Lincoln, Whyte, Davies, Tuck, El-Abd, Field, Muitt, Block, Sekajja, Wood, Swallow. Subs- Beck, Lea, Scutt.
Concord: Wells, Smith, Brown, Nasha, Roast, Knight, Da Costa, Lee, Greenhalgh, Cawley, Taaffe. Subs- Topley, Farrell, King, Akinwande, Marsh.
Ref: Ian Fissenden (Gillingham)