With Atletico having lost four successive league matches for the first time since Simeone took charge in 2011, the Argentine's role has come under scrutiny from both club supporters and Spanish media.
After the match, Atleti's Koke told reporters: "It's difficult. The other day we played a good game, today we played a good game and in two moments we lose the game.
"The team created chances, they turned up, they fought, you can't ask the team for more, just the results. It's the small details that are all going against us this season, like with our goal that was ruled out."
It took less than two minutes for Joao Felix to fire Atletico ahead with a perfect low shot from the edge of the box, with the goal demonstrating why the fans had been urging Simeone to play the Portugal striker from the start more often.
But Granada equalised 15 minutes later with a stupendous long shot from Darwin Machis.
The indefatigable Felix desperately tried to score a second goal but he was frustrated by an equally determined Granada, who found the winner midway through the second half thanks to Jorge Molina.
Koke added: "The team kept going and had chances to draw or even win the game. The wins will come because the team is trying and we won't stop trying."
It was Granada's first win against Atletico since 1973, ending a 25-game winless streak.
Simeone's judgment is constantly being questioned as Atletico's usually rock-solid defence has now leaked in 22 goals in 18 games this season, with the champions keeping only five clean sheets in LaLiga during that time.
In contrast, they had conceded only eight goals at the same stage during their 2021-2022 campaign.