Langelihle Phili opened the scoring at the FNB Stadium in the 63rd minute before substitute Cassius Mailulla levelled with his goal on 75 minutes.
Da Cruz opted to use a more defensive 3-5-2 formation for this Betway Premiership tie that Miguel Cardoso's side struggled to truly break down.
Amakhosi remain unbeaten in the league from their opening three games of the new season after kicking off their season with wins over Kruger United and Sekhukhune United.
Speaking after the draw, the head coach explained it will take time for his team to reach their full potential.
"If you want to compare Chiefs and Sundowns, you can't compare. Sundowns players have been playing together for six or seven years, and here we are at Chiefs where we arrived one-and-a-half months ago," he said in the Citizen.
"Let us have time and we will improve step by step. It has been a good start to the championship (Premiership), but there is still a lot of work to do, especially in offence."
"For me it was a high level match. I have had the opportunity to play Wydad and Raja (when he was coach at AS FAR in Morocco) and today was a match of that level," added Da Cruz.
"Today for us it was a Champions League match and we played like a team in the Champions League."
Chiefs are next in league action away against Richards Bay on Wednesday.
Mamelodi Sundowns head coach Miguel Cardoso says he is open to further strengthening his squad after seeing his team held to a 1-1 draw with Kaizer Chiefs on Saturday.
Mamelodi Sundowns head coach Miguel Cardoso says the tactics employed by Kaizer Chiefs in Saturday's 1–1 Betway Premiership draw caught him off-guard.
Mamelodi Sundowns denied Kaizer Chiefs a third consecutive victory in the Betway Premiership after the two sides played to a 1-1 draw at FNB Stadium on Saturday.
Kaizer Chiefs winger Asanele Velebayi has revealed the emotional significance of Luke Baartman's first goal for the club, describing the moment as though he had scored himself.
