Tresor Tshibwabwa scored the only goal of the game at the Orlando Stadium after 58 minutes, while Pirates were reduced to 10 men when Nkosinathi Sibisi was dismissed with five minutes of the match remaining.
The result saw Riveiro's side slip to 12 points behind league leaders Mamelodi Sundowns, although with two games in hand.
The Bucs boss felt his side were in the game at times but they didn't react well enough to going a goal down.
He said on SuperSport: "It was a game before the goal and a game after the goal perhaps.
"Game under control, I think the game was close for us, it looked the goal was coming and in a corner kick, in a situation that should be under control they managed to get the lead.
"After that we didn't react well. We were disorganised with not much ideas. Maybe I'm wrong but the keeper only made one save in the first half, we didn't manage to have shots on target or not enough. That's why the 1-0."
Riveiro's side are next in action away to Kaizer Chiefs in the Soweto derby at the weekend.
“I think the game was coming for us before the goal, but after the goal we didn’t play well enough to deserve the equaliser,” added the head coach.
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