Colin Calderwood's side remain rooted to the foot of the table following a 2-0 loss in which they again pressed the self-destruct button.
The visitors took a fourth-minute lead when Paul Ifill rifled an unstoppable 20-yard shot into the bottom corner.
But Forest then spurned a host of opportunities to equalise before a howler from goalkeeper Paul Smith gifted substitute Shefki Kuqi a decisive late goal.
After Ifill's opener, Forest could have levelled almost instantly from a corner as Chris Cohen picked out Julian Bennett at the near post, where the full-back thundered a diving header onto the bar.
Nathan Tyson then narrowly failed to connect with a pacy low cross from Lee Martin as it fizzed across the face of goal.
Palace should have made it 2-0 when a mistake from Wes Morgan allowed Craig Beattie to race clear of the Forest defence and fire into the middle where Ifill failed to convert from close range.
But Cohen then picked out Bennett from another corner, with the defender this time glancing a header narrowly over while Guy Moussi brought a save from Julian Speroni with a crisp shot from the edge of the box.
Forest came even closer to equaliser as Bennett powered into the box from the left and tried a lofted shot that Speroni clawed away acrobatically.
In first-half stoppage time they had a decent claim for a penalty rejected when Martin pounced on a loose ball in the box and appeared to have been brought down in clumsy fashion by Speroni.
Andy Cole was introduced after an hour to help Forest claw their way back into the match - but the home side were finding chances harder to come by.
Morgan saw his near post header saved as Forest continued to force a succession of corners. But it took a brave block from the defender at the other end to thwart Ifill as the Palace man went in search of a second goal.
And disaster struck for Forest when keeper Smith came charging off his line to claim a throughball he was never going to reach and, with the goal exposed, substitute Kuqi curled an angled shot into the empty net.