Fans reacted angrily to Simeone's decision to replace Rodrigo with 19-year-old debutant Borja Garces in the 71st minute as he looked to find a way to break down their stubborn visitors.
The Atleti boss had the last laugh, though, as Garces thundered home from 15 yards to snatch a point with almost the last kick of the game after Sergi Enrich had given Eibar the lead three minutes from time.
"The team understood that I wanted to win the game and I could have taken off Koke and Saul in place of Rodrigo," Simeone said.
"But I thought that they can create better transition in attack.
"The fans come here and they are very impulsive.
"They see a player doing well and I take him off. But the manager who works with them every day put on a striker and that player went on to score the goal to draw the game."
Atleti should have been out of sight long before Enrich's goal, but found Eibar goalkeeper Marko Dmitrovic in inspired form.
The Serbian produced a string of stunning saves to deny Antoine Griezmann, Diego Godin, Diego Costa and Saul Niguez.
Simeone added: "The team had chances to go in with an advantage at the break. Their keeper was spectacular. You have to congratulate him. We have to keep looking for these chances so the goal appears."