James Perch gave the Reds a second-half lead but they were pegged back when Alex Russell scored for the home side.
Caretaker Forest boss Frank Barlow told the club website afterwards: "Overall I am delighted with the point, a draw is about right. I always think we should win but overall it was right.
"It was a good, exciting end to end game with goalmouth incidents at both ends. We had to graft for it today, but we have done it and extended our run."