Forest were trailing to efforts from Kei Kamara and a wonder goal from left-back George Friend, but he sent on strikers Matt Derbyshire and Darius Henderson and they both scored to rescue a point for the Reds against a Boro side who finished the game with 10 men following the injury-time dismissal of Emmanuel Ledesma.
A delighted Davies said: "I said to the players at the end of the match that I was very proud of their performance, the effort, the commitment.
"The one thing we an say about this group of players is that they never give in, they have a fantastic energy and spirit about them and that's what makes me proud. It was a fantastic game of football and a fantastic performance from Forest.
"We thoroughly deserved to win the match and on another night we would have taken three points.
"They were 1-0 up with their only shot at goal in the first 45 minutes and then went 2-0 up through a wonder goal. But even at that point I was still confident we would get something from the game."
Referee Phil Dowd's performance was one of the main talking points after a frenetic encounter, with a series of bizarre decisions, but Davies refused to talk about the match officials, saying: "I will not comment on the referee's performance. I have no comment what to make whatsoever."