Well, I think European rules are that the Top 2 leagues can compete in the Europa League. So, that means that, even for someone who can name more teams than most people (for all I know you made up Valladolid, Elche, Granada), there are still 8 that no one has heard about. And La Liga is failing those teams.
What do you mean that only "the Top 2 leagues can compete in the Europa League"? Most countries get three clubs in the Europa League qualifying rounds, and it takes a lot of qualifying round games to get the field down to 48 for the Europa League Group Stage. There are also clubs that drop down from the Champions League to the Europa League. Read https://en.wikipedia.org/wiki/2013–14_UEFA_Europa_League if you want more information about the Europa League. As for La Liga, I don't even watch it but I know the club names from looking at the table, and I've heard of some of the other 8 that I couldn't name off the top of my head. http://us.soccerway.com/national/spain/primera-division/20132014/regular-season/r21879/ has the table if anybody doesn't believe me about the club names.
I mean that teams in each nation's top 2 divisions (Premier League/Championship; Ligue 1 and 2; etc) are eligible to qualify for the Europa League through Cups, but not teams in divisions 3 or lower; sorry if I was unclear. This isn't a game of 'how many teams can you name'. I'm demonstrating that La Liga is failing Elche to the benefit of Real and Barca. While that might work for a League made up of independent clubs, MLS (as a league) exists only for the benefit of its 19-22 member clubs.
Do you have a source from UEFA saying that? I'm not saying you're wrong, but I'm wondering if you have proof, although it would be extremely hard for a third level or below club to qualify for the Europa League through a cup competition anyway.