At the gym it's hard to imagine me as an introvert (so I've been told). I call it socially awkward but in reality the madness (training) comes from my time alone, in study or deep thought. This time is extremely precious to me, and it's often the difference between a good/bad/mad/sad/happy/fun/productive/worthwhile day.
This is hard to understand, esp for extroverts. But realize the benefits of this time and take advantage of it. Lonely is not a negative, it's a false feeling that you "need" someone else (for comfort, validation, or a sense of belonging). Relationships of all kinds become greater when others presence are welcomed, wanted and enjoyed rather than "needed".
Her book "Quiet" is my next read and I'm excited to dig into it.
For all other introverts and extroverts, keep going on your path to being the best that you can be for your cause. Aim for excellence.