A goal from Jack Hobbs earned Forest their first victory since 2011 against their East Midlands rivals, a result which Davies insisted his side fully deserved.
"Derby matches are always tense affairs but it is a fantastic three points. Tactically and defensively we were excellent and we're delighted with the clean sheet," he told the club's official website.
"We missed some big players today, the likes of Kelvin, Nathaniel and Jamie but the players stepped up really well and deserved their win.
"Derby have had the bragging rights over the past few years. Now it is time that our fans had them and they should go and enjoy it now."
Nottingham Forest are currently fifth in the Championship table, level on 18 points with Watford, Reading and Blackpool.