Speaking after the 1-0 defeat which saw them drop to second place in La Liga, the former France international said: "I won't say I'm worried because I don't like that word, but if w want to win something this season, we need consistency."
Zidane left fuming after Real Madrid lose at Mallorca
Though Madrid were missing key players thanks to injury, Zidane, said this was no excuse.
He said: "There are players who aren't injured, we have more good players too.
"When it comes to their turn, they have to show that they're at the level to be here."
However, the performance was panned by the Spanish media who did not seem to think those players were performing to the standards expected of them.
Spanish media outlet Marca commented that Luka Jovic, James Rodriguez, Isco, Alvaro and Vinicius Junior all appeared to "disappear on the pitch."
Zidane said: "The problem is that we have to show every three days that we're good - That's the difficulty, we don't do it."
Marca wrote: "Luka Jovic, James Rodriguez, Isco, Alvaro Odriozola and Vinicius Junior were all thrown in from the start and they were expected to assume responsibility in the absence of several key players.
However, it was the complete opposite as many of Zinedine Zidane's fringe players disappeared on the pitch.
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On James: "He was thrust into the starting line-up against Mallorca and failed to provide the creativity that Real Madrid were crying out for."
On Jovic: "Another opportunity passed the striker by as he wasn't able to have any sort of influence on proceedings in Palma. He looked completely lost playing alongside Karim Benzema and couldn't score his first goal in a white shirt."
On Vinicius: "The youngster is beginning to partake effectively in the game with his dribbling and link-up play but, once he reaches the penalty area, he loses control. His decision making in front of goal leave a lot to be desired whether it's shooting or passing."
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