Sandile Mthethwa opened the scoring at the Moses Mabhida Stadium after just 17 minutes, but Usuthu were unable to add to their lead before John Karelse netted an equaliser deep into injury time at the end of the game.
The result left Zwane's side in fifth place with 43 points from 27 games - five points behind Kaizer Chiefs in third. Arrows are down in eighth place with 36 points.
"We missed a good few chances in-front of goal with (Mondli) Mbanjwa," Zwane said on IOL after the game.
"I don't know what (Thapelo) Mathloko was trying to do when they passed us the ball.
"I cannot blame them and be a sore loser. I am disappointed because this feels like a loss to us, but I'm still proud of the team."
AmaZulu had come into this match on the back of a 5-1 defeat of Chippa United but were unable to replicate that form in front of goal against Manqoba Mngqithi's team.
“We took our chances against Chippa in the last game and (Wednesday night), we should have scored at least three goals because we are a good scoring team,” said the coach.
"We are a team that knows how to create scoring opportunities, but our only downfall this season has been failing to take those opportunities."
