Madrid played their first home match of the 2019-20 campaign on Saturday but were held to a shock 1-1 draw by Real Valladolid.
Karim Benzema scored what Madrid thought to be the winner in the 82nd minute, but Sergi Guardiola struck his second goal of the season even later to salvage a commendable point for the visitors.
Little has gone the way of Madrid – or Zidane – in recent months, with their close season marred by the ugly Gareth Bale transfer saga, poor friendly performances and uncertainty around some of the new signings.
Having finished last season 19 points adrift of Barcelona, Zidane knows the pressure has increased again this season and he is pleading for fans to lend their backing.
When asked if the team is under more scrutiny because of last term, Zidane said: "I noticed it at the Bernabeu - the crowd [feels the pressure] too.
"The fans also have to help us. There's no choice. I know it is difficult, but I'm asking because they have also taken advantage of our successes. We will try everything on our part."
On Valladolid's goal, Zidane lamented the lapse in concentration from his defenders that allowed Guardiola to score a late equalizer.
"It is not that we just lost the ball, something that it could happen at any time or in any place of the pitch.
"However, we were defending out of the mark, and that's not good. We scored, which is the most difficult, and then we should have booted the ball away, honesty," he said.
Madrid are next in league action on September 1, when they travel to Villarreal.