Jenner took home Olympic gold after winning the decathlon and was later named "Athlete of the Decade."
"My life changed with that one race. It changed everything," she told the magazine.
The former Olympian made the admission: "The decathlon for me was the ultimate in what people think of as manhood. So for me it was a good place to hide. I had a need to prove myself, that maybe that woman that's living inside of me really isn't living there."
The 66-year-old added: "I loved what I was doing. I was the best in the world at what I did. But I knew [the 1976 Games] would be the last time. I kept thinking, 'Hold on to the moment, hold on to the moment. Remember this moment, it's going to be over so quickly. You've got a long life to live after this.'"
It has been nearly 40 years since Jenner first appeared on the cover of the magazine, as Bruce, following the historic decathlon win.
The latest issue discusses her complex relationship with the piece of gold that made Jenner a household name, long before Keeping Up With the Kardashians.
"Sports. It’s not real life," she said. "You go out there, you work hard, you train your ass off, win the Games. I’m very proud of that part of my life. And it’s not like I just want to throw it out. It’s part of who I am. What I’m dealing with now, this is about who you are as a human being. What did I do for the world in 1976, besides maybe getting a few people to exercise a little bit? I didn’t make a difference in the world."
The magazine is tracing the steps of former Olympians prior to the Rio games in August.