Reds returned from Lancashire empty-handed as a 48th minute goal by Accrington Stanley's Shay McCartan handed them their third defeat in four matches.
Shay McCartan's early second half strike was lifted over the head of keeper Glenn Morris who needed treatment after bringing down the goalscorer.
Crawley made two changes to the side which drew 0-0 with Cheltenham, with James Collins returning from a one-match suspension and Josh Payne coming in for Rhys Murphy and Billy Clifford.
Reds started the sharpest as Collins seized on a defensive mistake but fired wide.
Kaby Djalo found Dean Cox, who cut-in from the wing but shot over the bar.
Accrington then produced chances at the other end as Billy Kee won the ball from Payne but fired straight at keeper Glenn Morris.
The Reds stopper was brought into play again to deny Jordan Clark with a bouncing shot from 30 yards.
Collins twice combined with Cox to create chances, the former Leyton Orient winger seeing his effort cleared then Collins saw his opportunity blocked.
Joe McNerney nodded an opportunity over the bar and just after Enzio Boldewijn's ball into the area was cleared only as far as Payne, whose ensuing shot was blocked.
Although Reds looked on top just before the break, Accrington scored within three minutes of the restart of the second half.
Billy Kee supplied a ball to McCartan who was brought down by the advancing Morris and the ball continued into the net for his 11th goal of the season.
There was a delay as the Reds custodian received treatment but then continued to play with a bandaged head.
The goal gave the home side a lift and Sean McConville soon nearly gave them a second goal with a far post header which flew over the bar.
Collins was on target with a chance which was deflected for a corner.
Accrington's McCartan hit the post with a curling shot with just 11 minutes left.
Crawley might have scored an equaliser with nine minutes to go when Payne launched a shot from 30 yards which was parried by the keeper to Collins who could not find the target.
Murphy came on for Jimmy Smith for the last nine minutes plus five minutes of add-time and pushed players forward but they could not find the net as Accrington extended their unbeaten run to 15 matches.
REDS: Morris, Young, Connolly, McNerney, Blackman, Smith (capt) (Murphy 82), Djalo (Clifford 62), Payne, Boldewijn, Cox (Roberts 62), Collins
Subs: Mersin, Garnett, Bawling, Lelan
ACCRINGTON: Rodak, Donacien, Hughes, Beckles, Rodgers, McConville, Conneely, Pearson, Clark, McCartan, Kee
Subs: Husin, Gornell, Boco, Edwards, Shaw, Brown, Chapman
ATTENDANCE: 1,652 (55 away)