...and of course it's not that simple...

One particular problem with HTML::Parser is that it has an XS component (compiled shared libarary code). This means you can't inline it into your script anyway. And, as far as I've understood from a quick look at the sources, App::FatPacker can't handle that either...

In other words, to build a stand-alone distributable program, you'd need a more full-blown solution, like PAR or perl2exe.