Griezmann has not yet made the mark he would have hoped for in the capital after making a big-money move from Real Sociedad.
Yet he was impressive after coming off the bench at Estadio Vicente Caldern - much to the delight of Simeone.
"Antonio Griezmann was very good, with great pace and with great speed," said the head coach after seeing goals from Tiago Mendes and Mario Suarez seal the points.
Atleti were not always at their best, yet showed their usual ability to grind out a victory.
He added: "The team was patient and that's how first the goal came. With the goal, we improved in the second half."
The main worry for Simeone was an injury sustained by goalscorer Tiago, who was withdrawn due to a muscle injury to the quadriceps of his left leg.
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