Try this:

my $response = $browser->post(
  'https://www.whatever.com/asdf.cgi',
  [
    'id'  => $id,
    'passwd' => $pass,
    'Input_tag_name.x' => 0,
    'Input_tag_name.y' => 0
  ],
);
[download]

UserAgent will put this into the form you want: Input_tag_name.x=0&Input_tag_name.y=0

"I was told that I must send this in the header"

I don't think this is precise, the data you post goes to the content, not the header. For get, it goes to the header.