I think the rules are pretty much the same - a good story, interesting characters and a cool visual output.
What's different about non hollywood film is that because they don't try to appeal to the lower denominator, they are built less on a patterns, or a formula and more as a personal experience, more artistic and less dogmatic.
There are many way to try and break out of the hollywood patterns, maybe indi films are not for you. Maybe you don't like the realistic look of most indi films or the plot was boring (I've never seen that film, so I can't really say).
One way at it might be by studying the history of cinema, try watching old classic westerns (the good the bad and the ugly, high noon) or american film noir (gilda, the postman always ring twice), or classic comedies (some like it hot) and see if any of them strike a cord.
Another way would be to try and see how you react to documentary cinema - there are a lot of really amazing ones done those days, a friend of mine keeps talking about "the devil and Daniel Johnson" I really enjoyed "spellbound.
Also, what might work for you is contemporary foreign film, I suggest trying the Asian ones, sometime the plots resemble Hollywood films but in a different style (I love 2047, 3 Iron, the vengance trilogy and many more) Also check out some Japanese animation film (Ghost in the shell, Akira, howl's moving castle, princess mononoky and so on) it's a totally different cinema experience.
Another option is to find a hollywood director or actor that you like and see if they made any less conventional films.
Also, remember that films in a matter of taste and not everyone need to like the same things, maybe the specific movie that you saw wasn't to your liking and another indi film would.
Hope this help, let me know how is it going.