Griezmann has endured his longest run without scoring a goal for Los Rojiblancos since arriving from Real Sociedad in 2014, last finding a way through against Chelsea nine games ago.
A section of the Wanda Metropolitano jeered the France international when he made his way off the field 76 minutes into Saturday's stalemate with rivals Real, but Simeone has called on supporters to rally behind the misfiring forward.
"I have been taught that those who are in my family, I am with them to the death. And I will not change now," he told reporters. "Things within your family are resolved within the family. I'm with my family, while they are still there."
Asked about his side's overall display, Simeone added: "The first 30 minutes were very good. It is true that the team has anxiety. We are at a time when we do not have the easy goal, but I will take the first 30 minutes.
"We played a good game against a very strong opponent. We could have won and we have could have lost and that is the beauty of the game."
Unbeaten Atletico have now drawn as many matches as they have won in La Liga, keeping them 10 points off pacesetters Barcelona.