Two goals from Frederic Bulot were enough for the home side at the Valley as Michail Antonio netted for the Reds.
Forest are now 11 points off the play-off places in the Championship and manager Dougie Freedman felt his side paid the price for their huge efforts in recent weeks.
"To win five games out of six was a momentous effort, and we paid the price for that. It just caught up with us," he told the official club website.
"I felt we needed a little bit more composure - we had enough of the ball and enough chances."
Opposite number Guy Luzon praised matchwinner Bulot, saying: "He was magnificent in defence as well as attack. He deserved his success."