Galaxy took control of the contest in the opening half, with debutant Sphamnadla Ngwenya finding the breakthrough in the 19th minute, before Junior Zindoga doubled the advantage from the penalty spot in the 32nd after Thato Sibiya fouled Seluleko Mahlambi inside the area.
Cardoso admits defensive errors coupled with missed opportunities in front of goal ultimately denied his team progression to the next round.
"When you don't convert the chances you had and you make mistakes which put you down 2-0 in conditions which are difficult to cope with, it is difficult to recover from that. The mistakes were caused by a lack of concentration, there's nothing else to comment about."
Cardoso says his side showed improved urgency after the restart, creating more scoring chances as they searched for a way back into the match.
Despite the attacking pressure, Sundowns were unable to capitalise, with Galaxy’s goalkeeper Ira Tape producing key saves.
Cardoso concedes his team fell short when it mattered most.
The Brazilians responded with a triple substitution early in the second half, withdrawing Sibiya, Kutlwano Lethlaku and Tsiki Ntsabeleng in a bid to inject attacking momentum, underlining Cardoso’s intent to chase the game.
"We knew that the bench would help us when we had to manage the result if it was a draw, but we cannot make the mistakes we did in this kind of a match. 2-0 is a difficult scoreline to recover from."
Cardoso rang the changes to his starting eleven, making ten alterations following Wednesday’s 2-1 league victory over Orlando Pirates.
That result followed another demanding outing in the CAF Champions League against MC Alger, as Sundowns continue to juggle domestic and continental commitments.
"I will not speak about individual performances here, but what is clear, the eleven players on the pitch have to cope with the responsibilities in the match."