"Griezmann is still one of the family and I defend my family to the death," Simeone told reporters.
"Every single player needs to deliver, as you can't win a game with just a few footballers."
Griezmann, who opted to stay at Atletico last summer after the club were hit with a transfer ban, has not scored since Sept. 27.
He caused controversy last week by saying in an interview with French television that he would like to play in the same team as Paris St Germain forwards Neymar and Kylian Mbappe.
"Antoine is calm, the goals will come and he is playing well," added Atletico midfielder Koke.
Atletico and champions Real are locked on 24 points but lost further ground to leaders Barcelona, who are 10 ahead of the two sides from the Spanish capital.
Real have never won a league title since falling eight points or more behind the leading team but Zidane said his side were still not out of the title race despite this latest setback.
"I don't think the league title is far away, there are still many games to come and many points to play for. I'm sure Barca will drop points," Zidane said.
"We have to keep working hard. 10 points seem like a lot when you look at the league table but things will change, I'm sure we'll cut the gap. Barca won't always win and we have to be up there."
The first derby at Atletico's new stadium was the first time the two rivals had drawn 0-0 in the league since 2005 and the game had all the passion and intensity associated with the rivalry but both sides lacked the quality needed to win the game.
Zidane, however, said he felt Real deserved to take all the points.
"We played very well, we just were missing a goal. I feel sorry for the players as they worked so hard, but we're going to keep going and we played very well today."
(Reporting by Richard Martin; editing by Rex Gowar)
