I'm not sure you even need a regex to do this. What about using unshift to reverse your string?

use strict;

my $string1 = "abcba";
my $string2 = "abc1da";

if (&reverser($string1)){
    print "Matched! Strings are palindromes.\n";
    }
else{
     print "Sorry, the strings are not palindromes.\n";
}

if (&reverser($string2)){
    print "Matched! Strings are palindromes.\n";
    }
else{
     print "Sorry, the strings are not palindromes.\n";
}


sub reverser{
             my $temp = shift;
             my ($reverse, @temp, @temp2);
             @temp = split ('',$temp);

             foreach (@temp){
                      unshift(@temp2, $_);
                     }
             $reverse = join('', @temp2);
             $temp eq $reverse?1:0;
             }
[download]

Should do what you're requiring without using the regex. You're just running the array you've made from your string and reversing it using the unshift.