Mendilibar believes Lionel Messi's absence was key.
The Argentine has scored 20 goals in 11 previous meetings with the Basque side, but couldn't add to that on Tuesday night.
"Finally, we've earned a point here, a point that feels like a victory," the Eibar coach said.
"It went very quickly, it was half time before I knew it.
"I think we had some luck, with the missed penalty, and we took the one chance we had, but the players ran a lot and they're very tired.
"They were missing the best player in the world and they did miss Messi.
"Every time we have come here, he has scored a couple of goals. Today we didn't have this opponent.
"We know they're all very good, the best, but luck wasn't on their side today.
"Going ahead gave us life and we leave with a good feeling. That's good for our mindset."