The result at Loftus Stadium left Usuthu in eighth place with three points from their opening two Betway Premiership matches of the 2025/26 season.
While last season's sixth-place finish raised expectations, Zwane insists there is no need for panic.
"It's too early to be worried. The concern is when you don't create chances at all. We are creating them, now we just need to sharpen our finishing," said Zwane according to Sportswire.
"That will come with time, repetition, and polishing the finer details."
Zwane believes the tactical approach against Sundowns was sound, particularly in the opening stages.
"They were pushing their defensive line high, and that's what we wanted, to press high ourselves and create space behind them. We forced turnovers, but didn't take full advantage. That's where the application has to improve."
For the coach, playing one of the league's toughest sides so early is an advantage.
"You can't choose games. Even if we face another top team next, it's good for us. These are the matches where players learn the most at this level," he explained.
Zwane stressed that AmaZulu's focus now is on consistency and converting opportunities into goals.
"We have to keep applying ourselves the same way, but be more clinical. Once we get that right, the results will follow."
AmaZulu will look to bounce back when they host Marumo Gallants at Princess Magogo Stadium on 20 August, with Zwane confident his side can turn lessons learned against Sundowns into points on the board.