Colombian striker Brayan Leon opened the scoring for the Brazilians after just six minutes at Loftus Versfeld on Saturday and completed his brace with a second goal in the 64th minute.
The result saw Sundowns claim their place in the last eight as runners-up to Group C leaders Al-Hilal, with nine points from six games, with Rulani Mokwena's Alger eliminated.
Reflecting on the tie, Cardoso lauded a top-class performance that he feels could propel them all the way in the competition.
He told SABC Sport: "I think we made a wonderful match, wonderful. Understanding what to do in every moment of the game, Champions League is this, Champions League is showing the understanding of everything that's happening on the pitch.
"We knew that we had to make a strong start and we did, we scored a goal, we knew they would change the dynamics, try and bring something else, but we knew we had to keep the ball, play the game and try to find the second goal and not drop [deep]."
A delighted Cardoso added: "These boys deserve the world, I'm so proud, today I feel proud from the energy we had from the stands. I made an appeal from the fans to focus on what is important and not distract from the way and the togetherness we need to have.
“The Ubuntu spirit was on the pitch, in the stands and it united us – this is the family of Masandawana – that's all we have to be until the end of the season.”