You should not feel like a complete loser because the interviewers are just people like you and their decision says nothing about you as a person, they just think they didn't see what they were looking for, they may be wrong and even if they are not wrong, it says nothing about your potential.
That said I don't think any advice here will really help. I've been in a similar position years ago and you have to experience actually getting into one of these places and then realizing everyone's just the same as you to feel better about this. I'm in the opposite situation to you now and trying to get out of a large tech company and do my own thing. I would say keep applying if this is what you want and keep practicing the interview style questions - personally going over algorithms and data structures without any other motivation besides interviews is hard for me. If you can work on something of your own, even a game or something not important do so, because when you finally do get in to one of these companies, you might find out (perhaps sooner than you expected) that you want to get out and having experience doing your own thing might make that easier.
That said I don't think any advice here will really help. I've been in a similar position years ago and you have to experience actually getting into one of these places and then realizing everyone's just the same as you to feel better about this. I'm in the opposite situation to you now and trying to get out of a large tech company and do my own thing. I would say keep applying if this is what you want and keep practicing the interview style questions - personally going over algorithms and data structures without any other motivation besides interviews is hard for me. If you can work on something of your own, even a game or something not important do so, because when you finally do get in to one of these companies, you might find out (perhaps sooner than you expected) that you want to get out and having experience doing your own thing might make that easier.