The Portugal star also cut a frustrated figure in the 1-0 defeat to Betis but Zidane insists there is little cause for panic.
Father and son will be reunited, albeit on opposite sides of the ball, when Madrid visits the Basque Country club. As a result, the score remained at 2-1 by the final whistle.
After a goalless first half, in which both sides had hit the woodwork, Yannick Carrasco opened the scoring in the 46th minute.
Ronaldo came close to sending Real Madrid 3-1 ahead early in the second period after collecting a brilliant pass from Carvajal, but the attacker sent his low effort just wide of the post.More news: 2 militants arrested for attack on paramilitary in Indian-controlled Kashmir
Ramos did have the ball in the back of the Alaves net moments later, but the centre-back's header was chalked off by the referee following a foul inside the home side's penalty box.
The winless Basques had plenty of late chances at an equaliser after Manu Garcia pulled them level in the 40th minute, but Los Blancos clung to their advantage. However, Ceballos scored minutes later to restore Madrid's lead after a gift from Pacheco.
Cristiano Ronaldo returned for Real Madrid, who were looking for a home win after two consecutive draws in the Liga Santander in front of their fans on Wednesday, reports Xinhua news agency.
Ceballos' pair of well-taken finishes before half-time took Madrid back to winning ways, although they had to survive Alaves hitting the woodwork twice.
But the Alaves substitute's stab under Navas bounced away off the frame of the goal again and Madrid escaped with the points.