After matching the league champions stride for stride for most of the contest, Marcelo Allende finally broke the deadlock at the Moses Mabhida Stadium in the 83rd minute.
The result saw Sundowns reclaim their place at the top of the league standings with 38 points from 17 games, ahead of Orlando Pirates on goal difference.
Usuthu are down in fifth with 30 points from 18 matches played, level with third-placed Kaizer Chiefs, who lost 2-1 to Stellenbosch in their league tie on Tuesday.
Zwane told SuperSport after the match: “I am disappointed because the players gave everything.
“We executed the plan in terms of waiting for the right moments. We had poor decision-making at some points in the final third entries; some of the players will learn, but I am disappointed, obviously, with the dropped points.
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“We deserved at least a point in this game, although we weren’t playing for a point – we fancied our chances.”
Zwane added that his team needs to regroup after the manner of their defeat. “For us to concede just when the game was about to finish, we will take the positives from the game and move on,” he said.
“The group needs time; we are a work in progress, and the winning mentality is what we are trying to instil in this group.
“We cannot just let teams come here and collect maximum points—they must feel it. We felt we could have done better when it mattered and shown more killer instinct in front of goal.”