Jordan Chiles is reflecting on the complicated mix of emotions she felt when she narrowly missed her shot at an individual all-around medal at the 2024 Paris Olympics.

During the qualifying round, the gymnast, 23, finished in fourth place with a score of 56.065, just .067 points behind her U.S. teammate Suni Lee, who earned a score of 56.132. Simone Biles came in first place with a score of 59.566. The only non-U.S. athlete to rank higher than Chiles and Lee was Brazil's Rebeca Andrade, who logged a 57.700.

Despite finishing in third place for the U.S. and fourth overall, Chiles did not secure a spot in the all-around final due to the Olympic rule that only two athletes from each country can compete.

In an exclusive interview with PEOPLE to promote her new memoir I'm That Girl: Living the Power of My Dreams, Chiles recalled feeling both disappointed for herself and happy for Lee, 21, in that moment.

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"Those are feelings," she says. "Everybody has feelings and everybody goes through a lot when it comes to being shy of something, right? You're in a job interview and you feel like you did the most amazing thing, and it can be that one little thing that can make you shy of getting your job interview, your job in general."

"So I think having those emotions is normal," Chiles continues. "I had to navigate them. I had to figure out what's next. I had a whole team final, and I had to go and support them for all-around and all those things."

While she was excited to cheer on Lee — and Biles, 27 — Chiles says she still found herself questioning if there was something more she could have done in her training or performance to make the cut. "It was difficult to know that I was that shy of being in the all-around. I did think, 'What else have I done? Could I have done something different here?' There were a lot of things that were going through my head."

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As for Lee, Chiles says there were absolutely no hard feelings between the pair.

"I was just very proud of her. Suni had gone through a lot. She had complications with her health, and seeing her be able to come back and strive and be on that team just in general and making another all-around is just amazing. That's dedication. That's something that's very heartfelt," she explains. "And so I couldn't be mad."

She adds: "You can be very, very happy for somebody, but you can also be sad at the same time because, again, those are emotions and everybody has emotions."

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Chiles experienced another major disappointment at last year's Summer Olympics when she was stripped of her bronze medal in the gymnastics floor final. Immediately after her routine ended, Chiles' coach successfully challenged the judges' scoring decision, bumping her up to a bronze-medal finish behind Brazilian gold medalist Andrade and Biles, who clinched silver.

However, it was later determined that Romanian competitor Ana Barbosu should be awarded the bronze after the sport's governing board ruled that the inquiry into Chiles’ score had been submitted too late.

Since then, Chiles has continued to fight the controversial medal decision. When asked about the status of her appeal, she tells PEOPLE her legal team is "still working on handling that."

While Chiles has stood on the Olympics medal podium twice — for Team USA's silver in the team final in 2020 and gold in the 2024 team final — the gymnast says she is still hungry for an individual medal. "Of course an individual medal is something that a lot of people want. At the end of the day, when you make an event final, that's what your main goal is. And that is something I continue to strive for," she notes.

That still-to-be-chased goal, she insists, takes nothing away from the tremendous pride she felt in standing alongside her teammates following their triumph in the team final in Paris.

"That was a history-making podium, and I'm just very proud that I was a part of that," Chiles tells PEOPLE. "And now that people can look into history books and be like, 'This was a history moment,' and I can continue to shine and be my best version of myself."

I'm That Girl: Living the Power of My Dreams will be available on March 4 wherever books are sold.

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