Pirates have enjoyed a dream start under Zinnbauer, winning six of his opening seven matches in the Absa Premiership thus far.
However, the German is set to get his first taste of cup action when they entertain Wits at Orlando Stadium this weekend, in what could be seen as their last opportunity for silverware this season.
Having come off a fifth consecutive victory against Chippa United last weekend, Zinnbauer believes the confidence will put them in great stead but more so will be their work rate as well as the backing of The Buccaneers faithful.
"[Wits] is a very big team, a very good team – they have been playing internationally [in CAF Confederation Cup] and they have very big players with experience," commented the former FC St Gallen mentor.
"It's a team that we have to work hard to beat, but the chance is there. We now have good self-confidence and we continue with the same things we do now.
"Then, for me, I'm happy that we had [the game against Chippa]. It was an end-to-end game, a final game for me which is a cup game, and the cup is always one game only.
"We play at home and I hope the supporters come and give us the support that the team needs, and when we hear them I think we give more percent on the field."
Pirates were earlier this season bundled out of the MTN8 and CAF Champions League at the first round, before being knocked out by rivals Kaizer Chiefs at the Telkom Knockout quarterfinal stage.