Interviews are really tricky from the businesses side too. All sorts of things can cause someone to turn away a skilled candidate. That's not right or fair, but it's how things go occasionally. Maybe the role was filled earlier that week by an overzealous hiring group, maybe one of your interviewers was in a bad mood because they skipped lunch, maybe one of them was trying a new question and wasn't familiar with what to expect out of it and set the bar too high... The list goes on. Long story short, a "no" doesn't always mean you're not good enough necessarily, so don't take it too hard.

Another thing that I find reassuring is that many businesses are trigger happy on the "reject" button because of how high the training costs are to bring on a new engineer. It's not just salary - it's pulling aside a mentor, passing up on hiring someone else, potentially introducing bad code into a system, and for really bad employees it's still pretty hard to fire someone.

Keep at it! Sharpen your skills, keep trying, it does get easier with time and experience.