Forest found themselves a goal and a man down midway through the first half after Tommy Smith fired Rangers ahead and Radoslaw Majewski was sent off for his crude 23rd-minute lunge on Adel Taarabt.
But they hauled themselves level through David McGoldrick's fortuitous strike and defended heroically as the npower Championship leaders cranked up the pressure after the break.
Davies had no complaints about the red card shown to Majewski for an ugly lunge on Adel Taarabt, and instead praised the players who stayed on the pitch for their efforts.
"We had to play for 70 minutes with 10 men and when you work hard all week on your shape and that happens, it's a disaster," he said. "I don't think there can be a complaint, it's a clear airborne challenge. It was naive and stupid.
"But even with 10 men we looked dangerous and we deserve credit after our game plan was blown to bits. My back five were magnificent. It's a great point and a well-deserved one."