She has been the story of this year’s Wimbledon, attracting the largest British TV audiences of the tournament as well as lavish praise from Michelle Obama. But on the day that Cori “Coco” Gauff’s bubble finally popped, the 15-year-old American promised to come back stronger and better – and continue to dream big.

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A 6-3, 6-3 defeat in the last 16 to Simona Halep, the No 7 seed and a former world No 1, was no disgrace given that Gauff was the youngest player to go this deep into the draw since Jennifer Capriati reached the semi-finals in 1991. Gauff was also troubled by an unspecified illness picked up at the weekend, which robbed her of her pep and power, although she refused to use it as an excuse.

“It’s crazy how big this has gotten,” she said, smiling. “If somebody told me this maybe three weeks ago, I probably wouldn’t believe it. I learned a lot, and I still had fun even though I was losing.”

“I’m only 15. I’ve not nearly gotten or developed my game. I started tennis at six. I’m so excited to see, if I continue to work hard, what other success I can have in the future.”

Facebook Twitter Pinterest Coco Gauff insists her next ambition is just to finish high school. Photograph: Tom Jenkins/The Guardian

It promises to be an especially vibrant one. When Wimbledon opened its doors last Monday, Gauff was ranked as the world No 319. Three victories later she has catapulted up to 139 in the WTA rankings, as well as earning her £176,875 in prize money, and she certainly did enough against Halep to persuade her opponent that she will soar to the top.

“I think she has a great game already,” the Romanian said. “If she keeps going she will be top 10 soon.”

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It may not be quite that quick or straightforward. Under WTA rules brought in to prevent young players burning out, Gauff can play a maximum of seven more events until her 16th birthday next March. However, everything is certainly in place for her to kick on.

She trains part of the year at an academy in France run by Patrick Mouratoglou, Serena Williams’s coach, while she is also represented by Team8, the agency cofounded by Roger Federer. Her team have refused to discuss her potential earning power but fresh sponsors are already queuing up to join the sports firms New Balance and Head and the pasta manufacturer Barilla to endorse her.

In March the US business magazine Forbes estimated she would make $1m in 2019. Now that figure looks deeply conservative.

Quick guide Serena Williams fined £8,000 for damaging grass court Show Hide Serena Williams has been fined $10,000 (£8,000) for an incident on the eve of the tournament at Wimbledon, when she threw a racket and damaged one of the outside courts where players are allowed to practice. The American has won about 40 times that amount so far, by reaching the quarter-finals of the singles and the second round of the mixed doubles with Andy Murray, but it is an embarrassment for her in the middle of what has been a successful tournament and one full of promise. Other fines handed out included $3,000 to Fabio Fognini, for saying during his third-round defeat that he wished a bomb would hit Wimbledon. In 2014, the Italian was fined $27,500 for a series of acts, including damaging a court. Nick Kyrgios has been fined a total of $8,000 for incidents in his first‑ and second-round matches. Photograph: Tom Jenkins

However, Gauff insists her next ambition is merely to finish high school. “I probably could have been done if I didn’t play this,” she said. “My teachers definitely let me take a break a little after this so I could focus on my matches.”

If Gauff leaves Wimbledon with any regrets it is that she fell a touch short of the staggering level of play during her opening three matches, where she played with ice in her veins and fire in her forehand. But back on No 1 Court, where she blasted on to the world’s stage by beating Venus Williams a week ago, a combination of illness and nerves knocked her off kilter.

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The American failed to take advantage of Halep’s early wobbles on serve – including three double faults in one game – and while she hit shots that had the crowd gasping, a final tally of 15 winners to 28 unforced errors told its own story.

And it meant that her extraordinary journey, which began when Gauff was given a wild card into the Wimbledon qualifying tournament a fortnight ago, had finally come to an end. But seven matches later she can now count Michelle Obama, who sent her a tweet praising her performance, as a fan. “It meant a lot to me because I’ve looked up to her for a long time,” she added. “She’s such a role model. I was really shocked. I wasn’t expecting that.”

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A standing ovation from the crowd also stunned her. “It’s amazing,” she added. “But with all that’s going on, I still felt I was in a bubble. Yet I hope people learned that I’m a fighter. That I’ll never give up. And that anything is possible if you work hard and just continue to dream big.”

And there is no bigger dreamer than Gauff, whose ambition is to be world No 1. But after what we have witnessed at Wimbledon in recent days, who would dare bet against her?