I do job guidance for a TEFL school in Prague. You will need a degree to find a job in Asia. Most Asian countries require a degree as part of the visa process so there is little you can do without one. However, most schools all over Europe care more about your TEFL certificate and your experience than a university degree.
Of course I'm a little bias, but I recommend the TEFL school that I went to and now work at: TEFL Worldwide in Prague. The trainers are really experienced and just fun to be in class with. If you are going to do a tefl course in Prague, you should do this one. Check out the website: http://www.teflworldwideprague.com