Langelihle Phili opened the scoring at the FNB Stadium in the 63rd minute and Cassius Mailulla levelled with his goal on 75 minutes.
Fernando Da Cruz's side played in a defensive 3-5-2 formation that the Brazilians struggled to break down.
Speaking after the game, Cardoso explained that they had to try and alter their approach but didn't quite show enough quality to win the match.
"We obviously didn't come to face a five-man defensive line, which Chiefs played today, but we knew the coach likes to prepare in relation to the opponent, so we were prepared to analyse what was happening on the pitch," Cardoso said on IOL.
"It was important not to lose the match — both teams didn't want to lose the match today," the coach added.
"I think we went more towards the intention of wanting to win, and that's because we showed that capacity on the pitch, and Kaizer Chiefs understood that from a transition they could get a goal — and it did arrive, and sometimes teams win games like that.
"Overall, it was a beautiful football match, played with natural aggression reflective of the levels of commitment from the teams on the pitch," he said.
The result saw Chiefs move to seven points from three games at the top of the league standings, while Downs are in seventh with four points from two games.
Next up for Cardoso's side is a home tie against Marumo Gallants on Wednesday as Amakhosi take on Richards Bay.