The two teams played out to a 0-0 draw in a Champions League Group B match which was dominated by the Buccaneers at the Orlando Stadium, but they could not find the back of the net on the night.
"We are having mixed emotions because, on one hand, we are really proud of the players for the performance they put up," Davids said after the match.
"On the other hand, we are really disappointed to throw away the two points. We are really proud of the boys for dominating the African champions from start to finish," he continued.
The former Maritzburg United head coach stressed the importance of winning their home games at the Orlando Stadium where they usually dominate their visitors.
"We also know that we let ourselves down in terms of not taking our chances. It is something to build on. There comes a point where we really have to believe how good we are," he added,
"No team comes here at the Orlando Stadium and dominates us. That is what we need to believe. But turning these good performances into points and goals that is the target that we need to work on now," he explained.
Pirates remained at the top of the Group B standings level on points with Esperance with three matches left in the group stage.
"The result opens up the group because Horoya won. It is still in our hands and we need to reach our target of 10 points. We still have a chance to qualify to the next round," he concluded.
The top two teams from Group B will advance to the knockout stages.