Los Blancos were poor in the first 45 minutes and found themselves a goal down at the break, as Jonathan Silva put Leganes 1-0 up with the last kick of the first half. Madrid initially looked revitalised in the second, as six minutes in, Karim Benzema scored a rebound to draw his side level.
Early second half promise was as good as it got for Zidanes side though and the manager, now in his second stint at the club, admitted that his side must get better.
As quoted by ESPN, the Frenchman said: "For me as coach, and them as players, we must keep trying to play better.
"We can play better, and we must play better. The first half was not so good, the second half a bit better. Even if this might have been a bad season, we must all give a bit more".
Benzema proved a lively presence up front and Luka Modric controlled the midfield in the second half. Alas, neither players efforts were enough to earn their side the three points. With Spanish media reporting that Madrid are looking to replace Benzema in the summer, Zidane was questioned over whether the talk had affected the 31 year-old striker.
Zidane responded to say: "I dont know - youd have to ask him about that. [Benzema] is used to that, new players coming, but he has shown his personality and thats it.
"He is a fantastic player and this year what has changed is that he has scored many more goals, so I am happy for him".
With 26 goals already this season, Benzema would attract interest from major European clubs were he to become available at the end of this campaign. Zidane will be wary of his value to the team and will need to make sure he plays his cards right ahead of a busy summer transfer window for Los Blancos.