Robert Earnshaw's close-range strike after 67 minutes won it for Forest after Peter Whittingham's penalty for Cardiff had cancelled out Wes Morgan's first-half header.
Forest are now five points behind Championship leaders QPR with a game in hand while the Bluebirds have slipped to fourth, six points adrift of Rangers.
Davies said: "We played some wonderful football, created a lot of chances and thoroughly deserved to take three points.
"The game was a great advert for Championship football and, in my opinion, Cardiff are a little bit ahead of us in terms of their development but there were so many good things about us here.
"We had 24 hours less than Cardiff to prepare for the game but we looked bright and fit and showed great character and spirit."