Gabi scored late on to confirm the result in a match that Diego Simeone's side controlled easily throughout.
It proved a comfortable night for Atletico, for whom Gabi scored a late third following Griezmann's two goals, and they lifted the Europa League for the third time.
The veteran striker was handed a megaphone and sang "Te Quiero Atleti" - (I love you Atleti). Now we are in the UEFA Super Cup, so he could play four finals with us.
Unfortunately for Payet, as well as seeing his first ever major domestic final cut short by injury, the ex-West Ham man could also now miss out on a place in the French squad for the World Cup, which explains his reaction.
"On a personal level he will feel so much pride, so much excitement after making a dream he had searched for so long a reality", Simeone said.
Griezmann, who grew up near Lyon but left early to pursue his career at Real Sociedad, previously had just the 2014 Spanish Supercopa to show for four seasons with Atletico. On Wednesday, Griezmann's first goal of the night albeit came from a defensive error on Marseille's part, but it completely took the sails out of the French side.
Atletico Madrid's French forward Antoine Griezmann scores the second goal
Gil Marin added: 'If he decides that he does not want to continue with us, we have to respect his decision.
Griezmann, who may well have put in his last performance in the red and white of Atletico after being heavily linked with a move to Spanish giants Barcelona in the summer, paid tribute to Marseille after the match. "If he stays we'll keep growing because we are destined to keep growing".
"I've been working to experience such a moment for many years", Griezmann said after the match. "Simeone has taught me a lot, he made me become a better player and I hope I can keep improving every year, in every game".
The striker missed a penalty in the 2016 Champions League final against Real Madrid which his side lost in a shootout and that made him more determined to perform against Marseille.
Barca are said to be keen to activate a reported €100 million release clause in Griezmann's contract, but Atleti general manager Clemente Villaverde insists the Rojiblancos are desperate to retain him.More news: Messi: It Would Be Terrible If Neymar Joined Real!
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