United pair Brian Onyango and Deolin Mekoa were given their marching orders at Orlando Stadium last night, meaning they will miss the next two games against Baroka FC and Chippa United through suspension.
Pirates eased their relegation concerns thanks to goals either side of the break from Ayanda Gcaba and Dove Wome in Soweto.
"I think we started very well to unlock them the way we did in the first half. We've ourselves to blame for not taking our chances in the first half," said Davids, who suffered his first defeat as caretaker boss after previously winning three matches and drawing three across two spells this season.
"And on top of that conceding yet again in the set-piece. On one hand you want to say well done and great performance from the players for really carrying out the tactical instructions. Going down to 10 men we kept the same structure, we kept the same intensity and at times it looked like Pirates were 10 men.
"But on the other hand I want to say they've got to be more professional. They've got to be more streetwise, they've got to be more mature in terms of handling the situations."
The Team of Choice are eighth in the standings with 26 points from 23 matches, and are determined to get to the 30-point mark as soon as possible.
"We set ourselves a target to get 30 points in the next four matches," added Davids,
"We want to reach the 30-point mark as soon as possible. We don't want to be thinking too far ahead of ourselves. We want to take it game-by-game and yes, absorb, take this loss, analyse it, go forward and then just focus on the next game.
"One guy has already asked me about the younger players. These are younger players and we don't want to put big targets in their heads and they lose focus.
"Let them focus on the next game, let them focus on the smaller target and the small target is the 30 points and then we take it from there."