Torres was a late substitute in his team's 3-0 win over Marseille, and the experienced forward has said that landing the European crown was the perfect way to bow out.
The 34-year-old has made 44 appearances for Atletico in all competitions this season, but is leaving the Spanish giants this summer following the expiration of his contract.
"On a personal level it was a fantastic final and now it's time to enjoy my last game with Atletico, because the end is coming and I know it's going to be very difficult," Torres told beIN Sports.
"I feel a happiness that is hard to describe since, after a long time, the opportunity to return to this champion team became a reality and the dream I had as a child came true.
"I am proud to belong to this group of players that has changed the history of the club. This is not a title, it's much more, the beginning of something bigger.
"Belonging to this group is above winning any title, because they are hard-working and humble people who know what Atletico is about. I am proud of them and I dedicate this trophy to all the Atleti fans."
Torres returned to Atletico in 2015 having initially left the club in 2007 to play for Liverpool, Chelsea and AC Milan.