Yep - same problem controlling any grass weed in a grass lawn pretty much.  Poa pratensis is different from Poa annua - probably the main useful diff is that the former is perennial, the latter annual.  With an annual like Poa annua at least there is long term hope by ensuring that you don't allow it to seed - as the plant you see dies off and the new season's lot come from seed in the ground.  However, there is almost certainly a good stock of seed existing and it can, of course, stay viable in the soil for some years so they will still keep popping up inevitably!  As you have already noted, if you really want to get rid of it you are probably faced with removal (dig up or non-selective herbicide) and re-seed.  If you really want to better identify the Poa species in question, have a look at to help out.