Pirates looked like they had a good fight against the marauding Sundowns in the first half of their Nedbank Cup quarter-final as each team scored a goal, only to collapse in the second stanza.
The Brazilians went on to score three more without reply as Pirates went home with their tails between their legs.
After bowing out of the Nedbank Cup, the Buccaneers now only have a small chance in the DStv Premiership and can still win the CAF Confederation Cup.
"It was not good enough for us, but tomorrow is a new day," said Zinnbauer after watching his side suffer one of the most humiliating results against Sundowns since taking over as coach in December 2019.
"We have to focus on the next games. We have to focus to [other] tournament, CAF, and then we go forward. It's so. We have to accept it.
"It's not good for us. I am very upset, it's clear. The better was not enough today, we have to accept it."
Bucs will now switch focus to the DStv Premiership when they welcome Maritzburg United to Orlando stadium on Monday.