The Portuguese boss has come under criticism for his side's struggles in the league this season.
With just over half the 2025/26 season to play, the Brazilians find themselves a battle for a ninth-successive top-flight title, in second place behind current league leaders Orlando Pirates.
They are also still in contention for the CAF Champions League after reaching the quarter-finals, with a win over former Sundowns' boss Rulani Mokwena's MC Alger but saw their Nedbank Cup campaign cut short by TS Galaxy after Cardoso opted to rotate his squad.
Speaking to media at the launch of the Mamelodi Sundowns Soccer Schools project, Motsepe said that Cardoso is expected to remain with Sundowns for some time to come.
He said on Soccer Laduma: "We are a club that looks at a project in terms of its entirety. Our supporters have been with us a long time and we also look at our coaches to say 'we want to be with you for a long time, so that we can achieve our targets'.
"At this moment, we have a lot of support and faith in our coaching team. They've done a great job to keep the team together and also focus on the task at hand and take us to where we are right now.
"If there is a message I would say to the Sundowns supporters, it would be to say to the supporters we saw at Loftus against MC Alger, thank you so much for the faith and support they show to the team.
"That match was a do-or-die match and it would have been easy to not even come to the stadium or write us off. But they showed their support in terms of numbers and in terms of how they sang and stood by us.
"They carried us from that game to the crunch title game at FNB Stadium. As long as we continue to support one another through the tough times, I think Mamelodi Sundowns will continue to make them very happy in future."
Sundowns are next in action against Sekhukhune United at Loftus Stadium on Sunday.
Orlando Pirates' coach Abdeslam Ouaddou says he was proud with the way his team overcame rivals Kaizer Chiefs 3-0 in their Betway Premiership clash on Saturday.
Kaizer Chiefs co-head coach Cedric Kaze has called on his players to bounce back from their 3-0 Betway Premiership defeat to Orlando Pirates on Saturday.
Golden Arrows missed an opportunity to move into the top half of the Betway Premiership on Saturday, while Siwelele beat TS Galaxy, and Orbit College drew with Richards Bay.
Orlando Pirates stormed to a commanding 3-0 victory over Kaizer Chiefs at FNB Stadium on Saturday afternoon, with Tshepang Moremi, Oswin Appollis and Evidence Makgopa all on target in a dominant Betway Premiership display.
