Griezmann scored twice as the Spanish giants overcame Marseille 3-0 in Lyon on Wednesday night.
The 27-year-old France international has been heavily linked with a move away from the Wanda Metropolitano this summer, with Barcelona favourites to land his signature.
Antoine Griezmann scored twice as Atletico Madrid beat Marseille in the Europa League final
Following the victory, Atletico boss Diego Simeone gave Griezmann his blessing to leave
After the final whistle Simeone, who had to watch the victory from the stands, admitted the forward could soon be on his way – but insisted his side would improve without their talisman.
‘Antoine – if he stays we’ll continue to grow and develop,’ the Argentinian said.
‘If he goes then great, he’s given a lot to us over the years. Even without him we’ll continue to grow.’
Griezmann struck in either half as Madrid captain Gabi rounded off victory with a late effort. And as he now looks towards World Cup success with France, Griezmann was pleased to lift a trophy under Atleti boss Simeone.
‘I left home when I was 14 wanting to win titles,’ he said after the match.
‘I was determined to take the opportunity to win one tonight. I didn’t want to miss out. I tip my hat off to Marseille, they have a lot to be proud of.
‘Antoine – if he stays we’ll continue to grow and develop… If he goes then great,’ Simeone said
‘It was a dream of mine to win a title under Simeone and I told myself that this was my time.
‘I’ve been with Atleti for four years and now I have a strong bond – with my team-mates, with my fans. That’s why I give my all.’
Meanwhile, Marseille boss Rudi Garcia defended his decision to play Payet from the start despite admitting his captain was unsure about his fitness.
‘I chose to start Dimitri, one of our best players,’ he told reporters after the game.
‘Even diminished, he set up the (Valere) Germain chance. We also missed him from set-pieces as Atletico, if they do ever concede, sometimes concede from set-pieces.
‘We hoped that he’d be at 100 per cent and we gave him a fitness test this morning.
Fernando Torres was given the honour of lifting the trophy on his final appearance for the club
Dimitri Payet was left in tears as he watches Atletico Madrid lift the trophy he could have won
‘He was worried about playing and whether he’d be able to kick the ball hard. He didn’t aggravate the injury today, he just wasn’t fully fit. In matches like this you have to take risks.’
Payet had rolled the ball through to Valere Germain in the opening five minutes only for the midfielder to fire wide.
That paved the way for Griezmann to take centre stage, Marseille failing to truly threaten again until the latter stages when substitute Konstantinos Mitroglou hit the post with a header.
‘We missed our chance in the first half,’ Garcia added.
‘We had the best chance first up and then we made a mistake that cost us a goal. Against a team like Atletico you cannot afford to fall behind as it becomes difficult.’