The stumbling European and Spanish champions were sent packing from the King's Cup by Madrid minnows Leganes after losing 2-1 at the Santiago Bernabeu on Wednesday.
They sit fourth in the league, a remarkable 19 points adrift of runaway leaders Barcelona, and their problems were compounded on Friday by injuries to captain Sergio Ramos and midfielder Isco, who will both miss Saturday's trip to third-placed Valencia.
Real said Ramos had a calf injury and according to reports in the Spanish media the defender will be missing for two weeks, while Isco will be out for one week.
Zidane gave a message of defiance in a news conference on Friday amid repeated questions about the team's decline.
"If I thought my message wasn't getting through I would leave here tomorrow," Zidane said.
The Frenchman was only recently hailed as a master manager of Madrid's famously tempestuous dressing room for leading the team to historic back-to-back Champions League triumphs as well as ending a five-year wait for a league title.
His qualities as a coach have been thrown into doubt this season, however, as he has been unable to resuscitate his side, who have lost three and drawn two of their last eight games in all competitions.
Real's only realistic chance of saving their woeful season is in the Champions League, where they face runaway Ligue 1 leaders Paris St Germain in the last 16.
"Football is full of good and bad moments and I have to try and turn this situation around and I still feel strong," Zidane added.
"If I didn't, then there would be a problem. I am going to try to continue doing this job with hope and keep trying to improve as a coach. No-one is going to take away my enjoyment of working until the last day.
"It's the same for the players, this is not their fault. There are many factors to consider, not just the result."
(Reporting by Richard Martin; Editing by Toby Davis)
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