The France international put an end to questions over his future in June when announcing in a television documentary that he would be staying at the Wanda Metropolitano.
Griezmann, who lasted less than an hour of Atletico's 4-2 extra-time victory over Real Madrid in Wednesday's European clash, says that he is more than happy to continue working under demanding boss Diego Simeone.
"I stayed because there was a good project," he told Movistar. "I have confidence in this club, in Cholo (Simeone)... Today I saw that I was not wrong.
"I was a little bit drowned because it was my second game [back]. In the end the important thing was to get ahead on the scoreboard, we made a very complete final.
"We know that physically the two teams have not reached 100%, the key was the desire to win. It was time for us to win the UEFA Super Cup again, it was very important to start the season like this."
Griezmann scored 19 goals in La Liga last season, before netting four times for World Cup winners France in Russia this summer.