This solution is just if you really insist on using Perl; the Re: a one-liner for this trivial problem? suggestion using grep is better....

perl -pie '
BEGIN {
  open $fh, "<" , "littlefile" or die "Cannot read file";
  our %hash = map { $_ => 1} <$fh>;
}
print if not $hash{$_};
' < bigfile
[download]

All the above will go on one line. any minor bugs are your problem (chomps may be needed for example) :-)