Usuthu were beaten 2-0 by the league leaders at Moses Mabhida Stadium, with Relebohile Mofokeng breaking the deadlock before goalkeeper Darren Johnson accidentally turned the ball into his own net.
The result sent Pirates to the top of the Betway Premiership standings, three points ahead of defending champions Mamelodi Sundowns.
Despite the setback, Zwane insisted the loss does not derail AmaZulu's long-term ambitions.
"A win would have been a big morale boost because it could have pushed us closer to the top," Zwane said after the match.
"But we are still where we want to be in terms of our target of finishing in the top four."
Zwane was quick to acknowledge the quality of the opposition, describing Pirates as the standard-setters in the league at present.
"They are the best team in the country right now. We had to be very careful with our approach because of the quality they have," he said.
The AmaZulu coach also pointed to limited preparation time as a contributing factor, explaining that squad rotation was necessary.
Pirates arrived in Durban fresh from a trip to Bloemfontein, while Usuthu had just one day to prepare for the encounter.
"We only had one day to work with the players, so it was important to freshen up the squad. That's why we started with players like Pule Ekstein and Bongani Zungu," he added.
Ekstein marked a significant milestone by making his 100th appearance for AmaZulu in the match. Zwane admitted the magnitude of the occasion may have weighed heavily on his players.
"We saw the opportunity to go top of the table and maybe put too much pressure on ourselves. We wanted to change the history against Pirates and make our supporters proud," he concluded.
AmaZulu will now aim to respond when they face Polokwane City away in the Nedbank Cup last-32 on Tuesday.
Relebohile Mofokeng has revealed how Orlando Pirates cracked a stubborn AmaZulu defence to secure a crucial 2-0 victory in Durban, moving the Soweto giants to the top of the Betway Premiership.
Siwelele FC have announced the signings of midfield duo Mahlatse Makudubela and Maloisane Mokhele as they look to improve their position on the Betway Premiership table.
Nigeria international goalkeeper Stanley Nwabali has parted ways with Chippa United by mutual agreement after three and a half seasons with the Gqeberha outfit.
Orlando Pirates head coach Abdelsam Ouaddou has called for a more competitive Betway Premiership, warning that prolonged dominance by a single club could harm the league's appeal.
