We can all identify with Julie to some extent because, as a social species, we are all genetically programmed to seek the approval of others. Oh sure, we are told that we shouldn't care what others think or say about us, but try as we might, we still do. We've all heard that old saying, "Sticks and stones can break your bones, but words can never harm you." Nothing could be further from the truth. It's actually quite the opposite.
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Concern about the opinions of others is so basic that I won't make claims that you can rid yourself of such feelings entirely. You can reduce them by making a conscious effort to see the reality of the situation.
To start with, recognize that other people are interested mainly in themselves. After you win they may congratulate and compliment you, and after you lose they may commiserate, but these are just social niceties.
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How deeply concerned are they really? Not very, I would venture. They would be more engrossed if the topic were their tennis rather than yours. You can appreciate this by turning the situation around. How emotionally involved or even interested are you in their tennis losses or wins? Of course you may not admit it aloud, but higher on your list of priorities is what you are going to have for dinner.
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Moreover, your true friends will value you equally whether you win or lose. Anyone who doesn't is not worth having as a "friend," and if you're smart you will keep your distance from such people because they are likely to be shallow, insecure and somewhat parasitic. (The only people who significantly and selflessly care about whether you win or lose are your parents, and that may be mostly because they know you enjoy winning.)
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So if, during play, you find your thoughts drifting towards what others will think if you lose, pause for a moment and say to yourself, "They couldn't care less! I'm playing for myself."
And if you were wondering, Julie worked her way back into the top 100 and was again being talked up by the press and the other players. This time, however, she had a more accurate assessment of such praise as superficial and meaningless.
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