Jordan Cousins scored late on for the visitors, who are now 21st in the Championship with three games in hand over Yeovil Town, one place below them.
Marvin Sordell came close to scoring for the visiting Addicks, but his effort could only find the post on 26 minutes after Cousins had teed his teammate up.
Simon Cox hit the post towards the end of the first half for Forest before Henderson was denied in stoppage time with a header.
Cousins netted the winner nine minutes from time when he converted into the bottom corner after finding some space for the shot inside the box.
Jamie Paterson's free kick sailed over the bar late on as Forest searched for a late equaliser.