LWP::Simple doesn't support the POST method.

Well, it sorta does, with a couple of extra steps:

use LWP::Simple qw($ua);
my $content = $ua->post("http://www.example.com",
  [first_name => 'Randal', last_name => 'Schwartz'])->content;
[download]

Of course, all you're getting here is a LWP::UserAgent created for you, and the right modules brought in with one use line.