I'd be inclined to use the "does not match" feature of !~:

#!/usr/bin/perl

use warnings;
use strict;
use Data::Dumper;

my $string = "asdfxyzasdf";

print "Not found\n" if($string !~ /xyz/);
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Of course, that assumes a regular expression is the best way of (not) matching your string -- if it's just a simple string, then the perl function index() may be more suitable.

Edit: Changed wording to more accurately reflect test.