Real are now four points clear of Valencia in the table as they look to guarantee a top-three finish, with Zidane determined to remain positive in the quest to catch Barcelona, who are 12 points ahead of his team.
"This victory leaves me with a very special taste," the coach said. "[Eibar] were better, they had a great game. It's a tough place to go and they played well.
"We knew that we were going to suffer and suffer. We had difficulties with the ball but we fought with character and got the win.
"Until the end, the league is possible, and not only for us.
"If you get distracted, you pay for it, so we must continue. If we want something, we have to win every game.
"Now we can rest, be with our families and prepare for the next game."