Amakhosi took a 10th minute lead at the FNB Stadium through a 10th minute Gaston Sirino penalty as Pirates right-back Deano Van Rooyen was adjudged to have brought down Pule Mmodi inside the area.
Evidence Makgopa then levelled in the 17th minute with a powerful header from a pin-point Dean Hotto free-kick but Yusuf Maart smashed home an 80th minute volley to claim a 2-1 victory.
For Chiefs' it was a first trophy in 10 years, and speaking after the game, Riveiro admitted that unlike in last week's Soweto derby win, his side was unable to come from behind to win.
He also felt his team deserved a penalty of their own - for a foul on Relebohile Mofokeng.
Riveiro told SuperSport: "It was an ugly match, there was not so much football from both sides. We were fighting the elements, and the game was affected quite heavily by the penalty.
"We had to come back again. And we managed to do it.
"In the first half we were territorially superior, we only had some problems with Mmodi, everything else was under control.
"We had an opportunity to score a second, with one action of Rele in the box. But we were not rewarded with a penalty."
Riveiro added: "In the second half the game was even more ugly, more physical, with more interruptions. In the last 20 minutes both sides with substitutes made the game a bit more open. And in that moment they scored the second goal. It was impossible for us to generate enough in the last ten minutes."
"Congratulations to Chiefs for the trophy, and that's it," concluded the departing Bucs boss, who guided his side to two previous Nedbank Cup titles.
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