But Benzema levelled up in the second half, heading in Marco Asensio's cross.
Asked to confirm that Bale would be at the Bernabeu next season, Zidane would not say.
Despite picking up three points, Madrid really struggled against mid-table opposition and were spared embarrassment by their French striker, who scored the victor with nine minutes left.
"This season we will not win anything, we know that, and playing for nothing is hard, and all that is said outside does not help".
Nacho started in defence alongside Raphael Varane, with Karim Benzema getting both the goals in the 2-1 win.
7 - Zidane pre-game claimed his players' "pride" should ensure a good performance but some of his biggest players appeared nearly embarrassed by the lack of anything to play for. "People's perception of him has changed as a result, but he's always been a crucial player". There's been up and down already under their new manager and now they are about to lose their most important player.
Madrid, who are placed at the third spot and 13 points behind leaders Barcelona, will next lock horns with Leganes on April 16.
He rested captain Sergio Ramos and dropped Toni Kroos and Casemiro to the bench in favour of inexperienced Uruguayan midfieder Federico Valverde, while bringing Spanish youngster Sergio Reguilon back in for the suspended Marcelo.
Among Madrid's worst performers in the first half was reportedly-unsettled galactico Bale, who was whistled even before missing an early one-on-one with Eibar keeper Marko Dmitrovic.
MF Toni Kroos, 7 - Got the ball moving forward quicker when replacing Modric, and provided the cross after a short corner from which Benzema Headed in the victor.
Benzema could have a hat-trick in the latter stages, but the he struck the upright from close range in second-half stoppage time.