Real took a step closer to a third straight European title after Marco Asensio hit the winner in a 2-1 first-leg come-back victory in Munich on Wednesday.
But having suffered an almighty scare at home in the quarter-finals, when Juventus won 3-1 in Madrid after Real had beaten them 3-0 in Turin, Zidane says nothing is decided despite Real's slender advantage.
"We will have to fight in the second leg, nothing is decided, that showed in the second leg against Juventus," said Zidane.
"We will have to suffer again and face Bayern in a different way at home, because if we don't, we could have a bad result next week," he warned.
The hosts took the lead at the sold-out Allianz Arena through Joshua Kimmich, but Marcelo equalised just before the break.
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Substitute Asensio hit Real's winner after finishing a counter-attack to seal Real's sixth straight win over Bayern in the knock-out stages of Europe.
"We can be happy with the result, we had difficulties at the start of the match in imposing our game," said Zidane.
"It's not easy to come and win here, we can do better, but we're happy with the result."
Zidane pulled a surprise before kick-off by dropping Gareth Bale, but insisted he does not have a problem with the Welshman.
"I have a lot of quality players here, he has been playing well and I know I can count on Gareth Bale the same way I do those others who also didn't play," said Zidane.
Toni Kroos was unimpressed with Real's performance at his former club.
"It was an average performance from us in the end, we had a lot of work to do, a lot of running," said Madrid's Germany midfielder.
"The result is good, nothing more than that.
"Bayern were probably a bit better than us, but we took our chances well."
Bayern captain Thomas Mueller admits the result does them no favours.
To compound Bayern's woes, they could have lost both Arjen Robben and Jerome Boateng for the return.
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Both suffered leg injuries in the opening half an hour and will be examined on Thursday.
"Madrid is Madrid, we saw their how coolly they took their chances," said Mueller.
"We need another mentality in front of goal, which could have been very different in my opinion."
Mueller says last year's 2-1 second-leg win over 90 minutes at Madrid in the quarter-finals -- before Bayern eventually lost 6-3 on aggregate after extra-time -- gives them hope.
"We won't give up, we won there last year, but we need a different mentality and a killer instinct," he said.
Bayern coach Jupp Heynckes was not happy to see his team throw away the lead and waste a string of chances.
"It was a curious game, we had a lot of chances we didn't use, so it's no wonder we lost," fumed Heynckes
"I'm not accusing anyone, but our defence was poor for the goals they scored -- we gave them away.
"What team has so many chances against Real and doesn't use them?
"We have nothing to lose in Madrid and go there with a free spirit."
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