Eibar had not taken a point or scored a goal against Real at their famous venue before Sunday when Fran Rico put the Basque side ahead.
Gareth Bale equalised for Real to secure the European champions' fourth successive draw in all competitions.
"This was an historic draw at the Bernabeu," Eibar captain Daniel Garcia told Spanish radio.
"We got into the jacuzzi of the Bernabeu because these are photographs that will remain in our memory. When we are older, we will remember days like this one."
The point lifted Eibar, who have won three of their seven games this season, to eighth in the La Liga standings.
(Reporting by Adriana Garcia, editing by Ed Osmond)
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