Pirates were two goals down at halftime after Bienvenu Eva Nga and Deon Hotto gave Wits a two-goal cushion but they fought back in the second stanza and forced extra-time thanks to Thembinkosi Lorch and Happy Jele.
The Buccaneers were close to sealing a come-from-behind win after Zakhele Lepasa put the side ahead just before the second period of extra-time but the Clever Boys snatched the equaliser in stoppage time of extra-time courtesy of Gift Motupa, before going on to win on penalties.
"Ja I'm not happy, we're not in the cup now, we have a big chance, compliment to the team they come back against Wits, it's not a small team, it's a big team and when you come back, we conceded two goals and then you come back and then you go in front, normally you have to win," Zinnbauer said on SuperSport TV after the match.
"But it the same what I said for the last six weeks, we need time for work, the mood is good, we're fighting, top game for the supporters, we opened the game but normally you can't lose this game."
The German mentor went on to explain how they turned the game around in the second stanza, particularly after they brought on attacker Kabelo Dlamini in place of midfielder Siphesihle Ndlovu.
"We changed our system what it was in the first-half, we were not in the game, not the leader, we [did not] dictate the game, the second-half was out of phase, this was Orlando Pirates but ja, we are not in the next round and that is for me, I'm not happy today."
"We conceded two goals and we had a player on offense, Ndlovu is not that type, we wanted more offense." he added.