The Los Blancos surrendered their unbeaten start to La Liga this season after a 1-0 defeat to the newly-promoted side at the Son Moix stadium.
The visitors were hit with a double whammy after Alvaro Odriozola was given a second yellow card in the 74th minute.
Real Madrid failed to remain top of the La Liga table after their latest defeat and have now been replaced by bitter rivals Barcelona, who comfortably won against Eibar.
The French coach said his side lack consistency and they need to adapt quickly to play very well in all competitions.
"The problem is that we have to show every three days that we're good," Zidane said. "That's the difficulty - we don't do it” – Zidane said after Madrid’s defeat to Mallorca.
"I won't say that I'm worried because I don't like the word, but if we want to win something this season, we need consistency."
"[I feel] bad because we didn't play the game we wanted and in the end, starting as we started, it has been difficult. In the second half, we were a little anxious because there had been no scoring chances."
The 13-time European champions went to the Balearic Islands without seven first-team players including their record summer signing Eden Hazard, who was left out to attend to the birth of his fourth child, and an injury list of Toni Kroos, Luka Modric, Gareth Bale and Lucas Vazquez but Zidane refused to use that as an excuse for their lacklustre performance.
"The injuries aren't an excuse," Zidane said. "There are players who aren't injured; we have more good payers, too.
"When it comes to their turn, they have to show that they're at the level to be here. We can't do anything about the injured players.
"We can't be surprised by a team playing in their own stadium. We knew what would happen. They surprised us because they scored, but then they backed down and we didn't find a solution."
Real Madrid are back in action with a Champions League match against Galatasaray on Tuesday.
