The Reds are five points adrift of safety after Ashley Barnes' early header condemned them to a 1-0 home defeat to promotion-chasing Burnley on Tuesday night.
Danny Wilson's men slipped a place to 23rd below Millwall who got a shock 1-0 win at Wigan while fourth-bottom Charlton beat bottom club Yeovil 3-2 to go five ahead of the Reds.
Barnes headed in Michael Kightly's cross on seven minutes then missed an open goal midway through the first half.
Barnsley failed to muster a shot on target with Dale Jennings' wild volley from 15 yards on 32 minutes being the closest they came. They have now not scored in four home games.
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