In my experience, the majority of people who interview at the big tech companies don't get offers. It's not even necessarily because the interviewee made any mistakes, just for whatever reason many companies like that are super picky because they can afford to be.

You shouldn't feel bad about it at all, but I know the feeling- it sucks, especially if you really got your hopes up. However, the fact that you got those interviews reflects very well on you, and the fact that you didn't get the jobs does not reflect poorly on you.

Just going through the interview process is a really useful learning experience. It builds confidence for future interviews and gives you a feel for how you might want to further develop your professional and/or interpersonal skills.

Sometimes job-seekers get lucky and get an offer right away. Sometimes people interview at 10-20 different companies before it works out. All you can do is not take it personally, learn what you can from each experience, and keep trying. If you keep trying you are guaranteed to eventually succeed (well, on an infinite timescale :), but if you give up you are guaranteed to fail immediately. Good luck!