Real are third in La Liga, seven points behind leaders Barcelona with seven games remaining, and were disqualified from the King's Cup in December for fielding an illegible player in a last-32 tie at Cadiz.
Zidane's side host ninth-placed Eibar in La Liga on Saturday and he is not expecting a backlash from the fans following their quarter-final defeat in Germany in midweek.
"I don't think the supporters will give us a bad reception. We know that on Tuesday we are playing for our season and so do our fans," the former France playmaker told a news conference on Friday.
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"I like challenges and so do our supporters."
Zidane, 42, succeeded Rafa Benitez as coach in January and again said his Real future was uncertain.
"A coach plays for his future in every game, I know the pressure at this club," he added. "But I don’t think about that, I am encouraged by what I'm doing every day.
"I'm always positive. If we lose on Tuesday it's part of football. I assume responsibility for this project and we'll see at the end of the season."
Zidane will be without injured French pair Raphael Varane and Karim Benzema against Eibar but is hoping they will recover to face Wolfsburg.
The coach has left goalkeeper Keylor Navas and midfielder Luka Modric out of the squad to face Eibar in preparation for the Champions League return leg.
Zidane indicated he might rest other players too but said top scorer and talisman Cristiano Ronaldo would keep his place.
Last weekend's Clasico win at Barcelona kept Real's slim title hopes alive.
"What we have to do is make sure we don't drop any more points," said Zidane.
"I won't say whether we can or cannot [win the league]. The best way to believe is to win."
(Editing by Tony Jimenez)
