A hat-trick from Victor Obinna cancelled out efforts from Dele Adebola and Dave McGoldrick for a Forest side who were the better team for large periods of an entertaining cup tie.
Davies said: "It's nice to come to the Academy of football and play the way we did in the first half. We lost a terrible goal after two minutes or so but then deservedly got in front and it looked as if their second goal was fortunate.
"We played fantastic football in the first 45 minutes - flowing, chances galore. In the second half we gave away a goal and after that we were chasing things. I am proud of the players. We showed fantastic stuff, but in the end it was down to experience."
Davies believed it demonstrated what Forest, currently in the Championship play-off positions, could expect to face in the Premier League.
"Look at their bench and it has got depth and quality," he said. "This is a fantastic football club with a great squad of players. We have got to realise that is what we are facing. In the first 45 minutes we looked a very good side, in the second half our inexperience and our tired legs showed, but it was a real big effort."