Atletico's hopes of advancing to the Champions League knockout stages were left hanging by a thread after the Azerbaijani titleholders held the hosts to a second consecutive draw in Group C.
Despite playing with a numerical advantage for almost 40 minutes, Simeone's side were unable to turn Thomas Partey's equaliser into a much-needed three points in the Spanish capital.
Atletico have now drawn each of their last three competitive matches 1-1 and have failed to score more than a single goal in their last eight outings.
"Explanations are excuses. We didn't start badly, we could've done more damage but weren't precise and Qarabag scored," Simeone said during his post-match news conference.
"We became anxious, nervous.
"The result isn't what we wanted and we know that right now we're having problems with scoring.
"Maybe in other years we have won games like this.
"When you score people talk about your strength, your courage. When you don't find that goal, people have a different opinion."
While Qarabag were unable to hold on for a famous victory, head coach Gurban Gurbanov was ecstatic that his team rose to the task against the 2016 finalists.
"[Atletico] played well, we all know their level, but my players didn't want to lose and showed their character," Gurbanov said.
"We're in a tough group, for us this is all about getting experience and learning. We've got two points but want to try and get more."