A couple of years ago, Mike the Mad Biologist compared likelihood statistics to falsification (he mentions the article today).
Let me first say that Mike is absolutely correct that likelihood statistics is a more productive approach for many many scientific problems. But Mike forgets, I think, that philosophy and working science have different goals and evaluate methodologies in different ways.
Regardless of what Karl Popper might have actually intended, he was not a professional scientist. Any scientist would be foolish, I think, to take Popper's writing as a guide to how to conduct an actual practical scientific inquiry on a specific question. Philosophers are usually — when they are doing anything productive at all — interested in creating the weakest possible definition for a term, the minimal definition.
I'm not a professional statistician, and I don't know that it's always possible to prove falsifiability from likelihood statistics (but I suspect that's the case). However, I can say that by Popper's definition every scientific inquiry using likelihood statistics is in principle also falsifiable.
Popper's falsifiability criterion is not necessarily the best way to do science. It is best viewed as the simplest possible way of distinguishing science from non-science. The falsifiability criterion has the advantage of not itself depending on any statistical assumptions. (Statistical assumptions are required, of course, when the hypothesis itself is statistical.) All that is necessary is that you have a way, some way, any way, of determining if the hypothesis were false.