The full-back predicted more trophies in the near future, while team-mate Javi Martinez branded the win his "happiest moment" as a footballer
The Bavarians lost twice at the final hurdle in Europe in the previous three seasons, but an 89th-minute winner from Arjen Robben secured a 2-1 win in an enthralling match against Borussia Dortmund.
Lahm believes Saturday's victory at Wembley will be just the beginning of a superb spell at the Allianz Arena, with a DFB-Pokal final on June 1 and a Bundesliga title in the bag.
"The pressure was enormous at the beginning. I've always said, if you want to be a golden generation, then you have to win an international title," the German full-back told Bild.
"Today, we finally succeeded. The team are at the right age and has good times ahead."
Javi Martinez was another star for the Roten against BVB and he says being crowned a European champion is the best experience in his professional football career to date.
"This is my happiest moment I can remembered in football in all my life, since I started playing aged five, through all of the times I've experienced in football," AS quote the midfielder as saying.