I think your approach is basically sound. I would do the details somewhat differently - avoiding some of the temporary variables - but that's just personal preference; I'd still use the same approach. I'd probably write something like:

use 5.010;
my $mess = "all letters are found";
my $_ = "...";
my $letters  = "...";
foreach my $l (split //, $letters) {
    $mess = "not all wanted letters found", last unless /$l/;
}
say $mess;
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