Manager Francis Vines says Crawley's play-off push has been ruined by poor finishing in front of goal.
Defeat at Aldershot leaves Crawley with a mathematical but unlikely chance of finishing in the top five with only three games remaining.
It was a case of what might have been because Crawley had enough chances to score before Darren Barnard settled it with 12 minutes remaining.
Dan Marney should have done better twice with tame side-foot efforts straight at keeper Nikki Bull in each half.
Steve Burton, with two goals in two games since signing from Scarborough, also squandered a hat-trick of opportunities in quick succession.
He took too much time to control a clever chip by Simon Wormull which released him on goal and his eventual shot was blocked by the covering Will Antwi.
He then flashed a header just over from a Neil Jenkins cross but the worst miss came a minute later when he looked odds-on to score after a flick by Marney sent him free on goal.
Burton's initial shot was saved by Bull with his legs and the follow-up was blocked by a combination of Brett Johnson's sliding tackle and Bull's desperate dive.
It is not the first time Reds have paid the price for wastefulness in front of goal.
Defeats by the odd-goal against Halifax and Dagenham and a draw against Leigh RMI in the last month were the result of missed chances.
Vines said: "We had opportunities to win the game but poor and weak finishing cost us dearly. The players, especially the forwards, have got to learn to take their chances. The reason we are not higher in the division is because we have missed too many good chances."
Other teams challenging at the top have proven goal-scorers. Morecambe were thought to be out of it after Crawley beat them in February but are now level on points with fifth-placed Halifax, thanks to striker Michael Twiss who has scored six goals in the last five games and 25 in total.
Champions Barnet, who secured their place in the Football League on Saturday, would not have raced away so easily without Guiliano Grazioli's 28 Conference goals, while Accrington strikers Paul Mullin and Lee McEvilly have 42 between them.
Crawley's top scorer is Allan Tait with ten league goals, 14 in all competitions, and he has been on the bench for the last three games.
Aldershot boss Terry Brown, who saw his side go fourth, said: "Sometimes the fine dividing line between success and failure is taking your chances when they come. It looked like we were not going to for a long time and we started to get a bit nervous."
The relief was audible around The Rec when former Wales international Barnard volleyed into the bottom corner from the edge of the box after a cross by former Lewes winger Dwain Clarke was headed skywards by Ben Judge.
Until then a mixture of luck, poor finishing and Andy Little's brilliance kept the Shots out. They could have scored four in the first half with Tim Sills heading inches over, Gary Holloway twice missing the target from close range and Nick Crittenden blasting horribly wide after being unmarked at the back post. Little made two superb saves in the second half, denying Crittenden with a point-blank block and then pawed away a close-range strike by Holloway.
Vines played tribute to defender Nick Burton, who started despite not being fully fit with a calf injury after a misunderstanding about Ian Simpemba's suspension.
Reds thought their captain had served a two-match ban and named him in the team, only to be told he was ineligible.
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