Atletico has reached two out of the last four finals -- Simeone's team were beaten both times by city rivals Real Madrid -- but Tuesday's draw in the Spanish capital leaves them in danger of failing to qualify for the tournament's knockout stages and dropping into the Europa League.
Beaten at home by Chelsea in their opening group game, Atletico has drawn their next three matches, including two against the Azerbaijani champions, playing their first ever Champions League campaign.
That means Simeone's men have to beat Roma at home and Chelsea away in their final two games, and hope Qarabag continue to pick up points against the odds, to have any hope of progressing to the knockout stages.
Under Simeone, Atletico's strength has been their defense.
Atletico hadn't conceded in 16 out of 19 Champions League games at their former Vicente Calderon home, but they've already let in goals in both matches at their new Wanda Metropolitano stadium.
Set pieces have also become a problem for the Spanish side and when Michel gave Qarabag a first-half lead it was the seventh time Atletico had conceded a headed goal this season.
At the other end of the pitch, it's also been an uphill battle.
Atletico is currently operating under a FIFA ban on registering news players until January, so club record signing Diego Costa and Vitolo can't play until the New Year.
Simeone's team has had 32 attempts on goal — the most of any side in the Champions League this season — but has managed to score just once.
It took 236 minutes for that goal to come, with Thomas Partey ending the goal drought with a long-range strike that pulled Atletico level on Tuesday.
"We have always played the same way," Simeone, whose Atletico contract runs until 2020, told reporters.
"In the past six years we have won 30 or 40 games like this and the only difference is when you score the goal people talk about strength and spirit and, when you don't, they see the more negative part."
"I believe you get what you deserve," added Simeone. "We have to try to beat Roma and then destiny will decide if we deserve to continue or are eliminated."
Club captain Gabi added: "What hurts most is that we don't have matters in our own hands, that is the cruel reality.
"We have to try and beat Roma and hope Qarabag are capable of holding Chelsea.
"At the moment we are out. We have a chance but it is very remote."