Real set a Spanish record of 40 games unbeaten in all competitions earlier in January and remain top of the La Liga standings by a point with a game in hand on title rivals Barcelona and Sevilla.
A first league defeat of the season by Sevilla and a 2-1 loss to Celta Vigo in the Cup removed the team's veneer of invincibility, however, and Saturday's unconvincing 2-1 win over Malaga did little to stem the criticism, with Real's supporters booing their players during the game.
"Listening to some of these questions you'd think we were battling relegation," Zidane told reporters ahead of Wednesday's trip to Celta Vigo where his side need to overturn a 2-1 deficit to advance to the semi-finals.
"I'm not worried and neither are the players. We're in high spirits," the Frenchman added. "Tomorrow we have a really exciting game."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Celta rested players in their league defeat at Real Sociedad at the weekend in preparation for the second leg and Zidane will field a full-strength team.
"We're going to try and win everything we have in front of us and that's not going to change, we're not going to throw in the towel," he said.
"If we don't win (the tie) it wouldn't be our biggest failure, although I'm not contemplating that at the moment."
Real are missing six players through injury with Colombia international James Rodriguez ruled out unexpectedly after straining a calf muscle just after recovering from another leg problem.
Midfielder Luka Modric and defender Marcelo sustained injuries against Malaga while full back Dani Carvajal's absence means out-of-favour left back Fabio Coentrao has been called into the squad.
(Reporting by Richard Martin, editing by Ed Osmond)
