The visitors looked to be cruising when two first-half goals from Kris Boyd, one of them a penalty, put them in command by the break, but City roared back to level through headers from Marvin Elliott and Jon Stead before Luke Chambers nodded home from a corner to give Forest the points.
An angry Davies said: "I have used a very loud voice in the dressing room because we can't hope to get anywhere playing away from home like that.
"It's all about keeping clean sheets and we also need to be much more ruthless in front of goal to kill opponents off. The players didn't start the second half properly and I have let them know that.
"We didn't stop crosses or headers well enough and allowed Bristol City back into the game.
"The other side is that we could have had four or five goals with better finishing, but we are still a young team with a lot to learn and even after Luke's excellent goal we were not solid enough in seeing the game out."