I have played around with your program a little bit, here is my actual version, perhaps it is usefull for you:

#!/usr/bin/perl
use strict;
use warnings;

use File::Find;

my $dir = '\webdirectory';

my $nameOne = 'alpha beta';
my $nameTwo = 'charlie';

my @pages;

sub mySub {
    return if -d $File::Find::name;
    return if $File::Find::name !~ /\.html$/;

    my $text;
    open (IN, $File::Find::name) or die "Can't open '$File::Find::name
+': $!\n";
    {
        local $/;       # Slurp-Mode
        $text = <IN>;
    }
    close IN or die $!;

    if ($text !~ m/\Q$nameOne\E/ and $text !~ m/\Q$nameTwo\E/)
    {
        push @pages, $File::Find::name;
    }
}


find( \&mySub, $dir  );
print "$_\n" for @pages;
[download]

I'm sorry for not using File::Slurp here as suggested, but its not installed here until now.