Real suffered a shock 1-0 defeat at promoted Mallorca and had fullback Alvaro Odriozola sent off 17 minutes from time, FourFourTwo magazine reported.
Lago Junior’s superb seventh-minute strike – his first in La Liga – settled the contest to cap a thoroughly miserable day for Real.
Barcelona had leapfrogged the Madrid side earlier on Saturday with a 3-0 win at Eibar and now holds a one-point advantage over Real after nine games.
“The problem is that every three days we have to prove that we’re a good side,” Real manager Zidane said at his post-match press conference.
“That’s our problem and it’s what we’re not doing. We need to have more continuity.
“We did some things well, to be honest. But, in truth, we can’t play a game like that.
“I’m not going to tell you I’m concerned, but we need to have more continuity.
“We need to bring a bit more life to our play if we want to achieve big things this year.”
Although Real had won five and drawn three of its opening eight league games, it has struggled in Europe this season.
Real lost its Champions League opener 3-0 to Paris St. Germain before being held 2-2 at home by Belgian outsider Club Brugge.
its latest setback came with Gareth Bale, Luka Modric and Toni Kroos all sidelined by injury and Eden Hazard missing after his wife gave birth.
Karim Benzema struck the crossbar in the first half but Real was running out of ideas when it was reduced to 10 men by Odriozola’s second yellow card.
“Injuries are part of football. We had other players and they need to do better,” Zidane said.
“Having players out is the circumstances we face and we have to overcome that.
“There are other players, who are good. We need to show that every player has the ability to play here.
“We didn’t play the game we wanted. When we start a game the way we started this one it makes it tough.
“They scored, then they sat back and we couldn’t find the solution.
“We need to analyze it properly. We can’t be happy with the match.”
Real returns to Champions League action on Tuesday with a trip to Galatasaray in Turkey.
“We know what we’re playing for,” Zidane said.
“We need to play to win because there’s no other option there. We need to focus on winning on Tuesday.”
Mallorca’s third win of the season took them out of the relegation zone and in to 14th place.
Goalkeeper Manolo Reina had few serious saves to make, even though Mallorca had to defend for long periods.