In a game of few chances Graham Stack was the home side's hero as he tipped Medy Elito's fine strike onto the bar in the 70th minute to secure a second-straight draw at Underhill for the Bees.
But with three minutes remaining Barnet substitute Kyle De Silva was shown a straight red card for a high challenge on Daggers' Luke Wilkinson, while Barry Fuller was sent off after the final whistle for foul and abusive language aimed at referee Keith Hill.
"It seems that the referee said that Fuller insulted him, but I don't believe it," Barnet player-manager Davids said.
"If you don't play well, the referee can influence the game, and that's what he did.
"Kyle De Silva, it could be a red card. The tackle on Nurse was even worse, he really caught Nurse and his knee was almost open.
"I feel that lately the referees are not fair to Barnet, this is not the first time but back-to-back incidents where I have seen referees penalise Barnet, so then I think do they want us to fail?
"We have a difficult game ahead against Wimbledon on Monday, you never know how the referee is going to do the match - I don't know what instructions he gets from the FA.
"I do feel like this is personal against Barnet, and it's not the first time I've said it. Enough is enough. I don't like it, we already have a tough time and a tough period ahead and we can't have also this influencing our team as well."