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Barcelona's title defence was dealt a blow on Tuesday when they were held to a 2-2 draw with Atletico Madrid at the Camp Nou.
And Griezmann, who has struggled to replicate his Atletico form for Barca, was subbed on during the final five minutes of the clash.
Dugarry, 48, suggested that the 29-year-old French star's struggles came down to the lack of harmony with Barcelona captain Messi.
However, the former France international crossed the line for many fans when he called the six-time Ballon d'Or winner "autistic."
Dugarry said on French radio show RMC Sport: "What is [Griezmann] afraid of? A kid who is 1.5 metres tall and half autistic?
"All he has to do is show some balls at some point. I've been saying for a year that he has a problem with Messi. He has to hit him in the face.
"It's true that Messi could give him more passes, but honestly, I am not surprised.
"Griezmann loses balls, doesn't play with confidence. Griezmann should go and talk to Messi to solve the problem."
Dugarry took to social media after his comments sparked backlash and apologised for what he said.
But the 1998 World Cup winner would surprisingly delete his statement from his personal account.
"I'm sincerely sorry for the breadth and depth of my remarks about Lionel Messi," he tweeted.
"I didn't want to stigmatise people with autism disorders, that was not my intention.
"I apologise to the people I shocked and will do it again [apologise] on Team Duga [TV show] this evening."
Dugarry also pulled no punches towards Barcelona boss Quique Setien, who he branded as "incompetent" for his decisions made in the match.
"He is not a decisive coach. Setien is very nice but he doesn't have the right credentials - he didn't know who to change," he said.
"He replaced Sergio Busquets in the 85th minute to bring in Ansu Fati and launched Griezmann in the 90th.
"I don't think it's anything against Griezmann, he just doesn't know how to get this team to play. He's completely overwhelmed. I'm convinced that he has nothing against Griezmann, but rather he is just incompetent."
Atletico boss Diego Simeone was also stunned on the touchline when he saw Griezmann being brought late on against his former side.
Featured Image Credit: PA/RMC Sport
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