Lewis McGugan stepped off the bench to net the winner five minutes from time after Darius Henderson had cancelled out George Boyd's opener.
McGugan's fellow substitute Billy Sharp supplied the cross that led to the winner, which earned Forest their sixth consecutive victory.
"Sometimes it works for you and sometimes it doesn't," said Davies, whose side have not won seven in a row since 1922.
"That's the type of impact we need from subs. We certainly went out and tried to win the game.
"I thought we started not the brightest; we just didn't stick to our game plan and gave them too much space.
"They score a goal against the run of play, and second half we showed great courage and we went for it. We put on some very attacking substitutes and McGugan does what McGugan does best and gets the winner.
"We tried to win the game, especially at 1-1. We've given ourselves a great chance of the play-offs."