The Buccaneers took the lead in the seventh minute through Tshepang Moremi and Usuthu thought they were level when Mlondi Mbanjwa fired home midway through the first half, only for the assistant referee to raise the flag for offside.
Zwane's side were eventually handed a route back into the contest just before half-time after Kamogelo Sebelebele brought down Mbanjwa inside the box and Thandolwenkosi Ngwenya calmly converted his spot-kick.
Reflecting on the game, a disgruntled Zwane explained that he felt his side's disallowed goal should have stood.
"I don't think the goal that we scored was offside," he said on SuperSprt.
"We wanted to take the game to Pirates, we are playing at home. Yes, they will create changes, but we will create chances also and maybe we will bury some.
"Like I said, we scored a legitimate but unfortunately it was disallowed; that's football for you, so that is my belief at this time, I will double check again."
When further quizzed on his approach to the game, opting to attack Pirates rather than be more defensive, a bullish Zwane added: "We created few chances in the first half and second half that we could have capitalised on and one of our problems is that we didn't connect with the forward runners, and we have been working on this; that has been our downfall even last season.
"We defend well but we must know how to come out of tight situations and whenever we do that well we usually scored from those moments, but I thought we could have done better and even scored a winning goal."
AmaZulu next face Siwelele at home at the weekend.
