Zinnbauer, appointed following Mirko Slomka's sacking earlier this week, clapped his players off the pitch after frustrating the reigning champions.
Bayern dominated for long periods but could not break down a resolute home defence.
Thomas Muller and Jerome Boateng wasted chances, while on-loan Spurs player Lewis Holtby went closest for Hamburg.
The stalemate saw Pep Guardiola's side slip to fourth in the Bundesliga table on goal difference, level with leaders Padeborn, who they face on Tuesday.
Bayern captain Philipp Lahm has demanded an improvement from his team-mates when they face the newly-promoted side at the Allianz Arena.
"We can't be satisfied when we draw," Lahm said. "We could have won the game in the second half, but overall we didn't do enough."
Zinnbauer was proud of the efforts of his players as second-from-bottom Hamburg collected their second point from four matches.
He added: "A point against Bayern is a great result for a team in our situation. Everyone can see we're fit, and we had great team spirit as well."
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