In a goalless draw, the hosts dominated proceedings, hitting the woodwork four times - twice through Billy Sharp and once each through Andy Reid and Henri Lansbury.
Forest are two points out of a play-off spot with just a brace of games remaining and should have beaten a Barnsley side still inside the relegation zone.
Davies said: "I couldn't ask more from the players. You have all seen the post hit, the bar hit, all the chances we created, all the crosses and there's no doubt we deserved three points. Lady Luck was against us.
"At the moment the breaks are just not going for us but I said to the players after the game that if they take today's form into the last two games they will win them both.
"We are disappointed to have only got one but we will go into our last two games trying to win them both and that will take us to 70 points.
"I said before today that we needed two wins and a draw and if we can achieve it that might be just enough to get us in."