The spirited home side had chances of their own to claim all three points, but Griezmann insists he and his team-mates did not underestimate Qarabag as they remain determined they can qualify.
"It was never a given we'd win here," he said. "[Qarabag] are strong and we need to carry on working in order to score more goals.
"We made chances but knew it would be hard, that they'd drop deep and we need to be more efficient because we had our opportunities and we need to take them.
"We've still got three games to qualify and we'll fight to the end."
However, midfielder Gabi conceded that Atleti face a tough task to progress now, as they will likely require a trio of wins.
"In the first-half we had chances, while in the second period we tried but just couldn't score," he added. "This is a tough place to come and we didn't get the win.
"We had problems in front of goal. We had chances but they got a good point. We need to win the three games we have left."