Real were pushed all the way by the minnows before eventually winning 3-1, with Benzema again on the scoresheet.
Zidane said, "We played very well. Eibar also had their good moment. The team dug in at times and controlled the match well. We knew it's a difficult place to come, but we controlled it from start to finish.
"It's a battle that won't stop, we're playing every three days and we have to carry on like this. We have to enjoy the performance we put in here and prepare for the next one. We knew that Eibar play a more direct way and we had to press them higher up and we did it quite well.
"Benzema is a match winner because what he's doing is on a different level, not just because of the goals. I always repeat myself saying the same thing about Karim. It's not only his goals, he's a focal point in our game, he's very important for us and when he scores, he scores it's even better, obviously, but he's very important for our team. We have to highlight everyone's performance.
"It was a great game today and it a great performance from both teams. It's a well-deserved victory."