The Bees scored either side of half time with Elliot Johnson's low delivery allowing Kenya international Atieno to fire in the opener from two yards before John Oster finished a clinical counter-attack, following a horrible miss from Bradford's Nahki Wells, to seal all three points.
"Sometimes instead of giving away an equaliser, you get a goal, it's very good for us but we shouldn't have got into that position in the first place," said Davids.
"I am happy that we got two goals and some of our playing spells were unbelievable, sometimes you have to pass to get the opponent into submission.
"Our two centre-halves put in a very good shift. It's very hard to fight against a player like [James] Hanson, he's tall and that's just how they play.
"The result comes first, but I thought in spells you could see some of the play from training the whole week.
"To see them execute it, even under this high pressure, I think is progression.
"Despite my [shoulder] injury there has been no change in my approach, I trained with the group and before the injury I was always focussed on the team."