Greg Halford's early goal secured the points for the visitors at The Den to set up a tantalising last-day clash with local rivals Leicester for a place in the play-offs.
Davies took the Forest job in February with the team struggling in the Championship, but they have now gone above the Foxes ahead of the derby next weekend.
"Many people back then predicted we would need three points here to stay up," Davies said. "But now we go into a pre play-off play-off next Saturday.
"It's a very exciting time for everybody. The last day of the season will be a nerve-shredding time.
"To find ourselves in this position with one game to go, I'm proud of the players and the staff and hopefully we can get that three points and sneak into the play-offs.
"It's a fantastic end to the season. Roll on Saturday."