But if this season is to be his last with the club, Griezmann produced the perfect parting gift at the Groupama Stadium.
A Marseille error opened the door for the forward to put Atleti in front after 21 minutes, before a delightful finish doubled the advantage for Diego Simeone's men early in the second half.
The Ligue 1 outfit had started brightly but had their momentum checked by Griezmann's opener, and an injury to captain Dimitri Payet before the break came as a further blow to their hopes.
Their best chance to pull a goal back came 10 minutes from time, when substitute Kostas Mitroglou headed against the post, but Gabi wrapped up the victory with one minute remaining.
The lingering smoke of flares hung over the opening stages, and Jan Oblak will have been thankful to see Valere Germain lift an effort over after emerging from the clouds to run on to a Payet throughball in the fourth minute.
As the haze started to lift, Simeone – watching from the stands thanks to a touchline ban – will have seen his side continuing to come under pressure from a Marseille side who looked lively.
But it only took one Marseille mistake for the Spanish side to snatch an undeserved lead.
A calamitous touch from Andre-Frank Zambo Anguissa allowed Gabi to play the ball through for Griezmann, who slotted a simple finish beyond Steve Mandanda.
Lucas Ocampos sent a looping header just over from a free-kick after 24 minutes, but more bad fortune would soon follow for Marseille.
Payet, who touched the trophy as he walked onto the field before kick-off, limped off in tears after having recovered from a muscle injury to make the starting XI.
The loss of their skipper sucked some of the life from Marseille's previously spirited display and Griezmann's second, four minutes after the restart, felt like being the match winner.
Koke released the 27-year-old into the box and he lifted the ball over Mandanda to double his side's lead.
And after the post denied Mitroglou when he got on the end of Morgan Sanson's cross, any faint Marseille hopes looked to be over.
Gabi made absolutely sure of Atletico's sixth trophy under Simeone with a strike from the right side of the penalty area, as Koke claimed his second assist, and the departing Fernando Torres was then brought on for a glorious swansong in stoppage time.