The victory increases their play-off ambitions but the result was a severe blow to relegation-threatened Forest.
Furious Forest boss Davies said: "The first thing we should be doing is apologising to our travelling fans.
"We showed a lack of desire and commitment and I am very disappointed. You have to be born with a winning mentality.
"You cannot work on individual error or having a will to win and we have players who lack a will to win.
"We are a young side but Burnley knew how to play the pitch and the conditions."
Burnley suffered an early blow when striker Steven Thompson was carried off after six minutes to be replaced by teenage protege Jay Rodriguez.
But the Clarets went in front when a Robbie Blake free-kick from wide on the left evaded both attackers and defenders alike before nestling in the net.
And Burnley increased their lead seven minutes before half-time as Blake teased and tormented the Forest defence before picking out Wade Elliott to score.
Their third arrived six minutes into the second half when Graham Alexander's free-kick found Martin Paterson who crossed for central defender Clarke Carlisle to squeeze a header beyond Forest goalkeeper Paul Smith.
Rodriguez scored the goal of the game on 55 minutes when he collected a short pass from Blake and curled a sumptuous right-foot shot into the top corner.
The scoring was completed when Forest failed to clear a cross from Chris Eagles and Joey Gudjonsson thumped a volley into the net from the edge of the box.
Burnley manager Owen Coyle said: "There was never five goals in the game but the bottom line is we were clinical. All season we have been creating a host of chances but this helps the goal difference.
"We have got some gifted players in the offensive third of the field and we did try and get the ball down but the pitch is not helping us in the way we like to play.
"Rodriguez is banging on the door ready to start again, his level of performance is what I am looking for at this football club."