It could have been even worse for the 2014 and 2016 finalists had South African striker Dino Ndlovu won a penalty rather than being shown a second yellow card for diving 15 minutes from time.
Atletico now have just two points from their opening three games and remain third in Group C behind Chelsea and Roma, who were due to meet at Stamford Bridge later on Wednesday.
The visitors had a host of chances to open the scoring in the first half, but suffered from a familiar lack of firepower in already their fourth 0-0 draw of the season.
“The strikers have to work on it. We are good at the back, created chances and we didn’t take them,” Atletico forward Antoine Griezmann told BeIN Sports Spain.
“There are still games to go. We will try to win them all and see what happens.”
Griezmann and Yannick Carrasco were both denied by Ibrahim Sehic when clean through, while Jose Maria Gimenez fired inches wide from a corner before the break.
However, it was Azerbaijani champions Qarabag, in their first ever season in the Champions League, who had the better chances in the second period.
Ndlovu’s rising effort flew inches over the bar before he thought he had won a penalty as he was clipped by Diego Godin inside the area.
Instead, French referee Ruddy Buquet reduced the hosts to 10 men for what he thought was a dive.
Atletico pressed unconvincingly in the search for a winner and their best chance came when Fernando Torres headed over after he too appeared to be pushed with the goal gaping five minutes from time.
Buquet was unmoved, though, as Atletico’s European campaign continues to stumble after a stalemate away to Roma and a 2-1 defeat at home to Chelsea.