Griezmann has looked a shadow of his former self this season and was again anonymous in the derby stalemate at Wanda Metropolitano.
The France international has shouldered much of the blame for Atletico's scoring woes - netting only twice in 10 league games - and was greeted by jeers from the home supporters during his 76th-minute substitution.
Simeone refused to criticise the attacker, although he did hint that the 26-year-old may be moving toward the exit door.
"I have been taught that those who are in my family, I am with them to the death. And I will not change now," Simeone said after the match.
"Things within your family are resolved within the family.
"I'm with my family, while they are still there."
Simeone was full of praise for his side's start amid a charged atmosphere, but admits that anxiety has a tendency to creep into their game if they do not score early.
"The first 30 minutes were very good," he said.
"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."