It is easier to test explicitly for what you want.

use strict;
use warnings;
print "Enter a string: ";
chomp ($_ = <>);

my $msg
    = !/a/i ?    'String did not match'
    : !/a.*b/i ? 'The string has an a, but not a following b'
    :            'The string has an a, but also a following b'
    ;

print $msg, "\n";
[download]

UPDATE: Even better, use positive tests:

my $msg
    = /a.*b/i     ?  'The string has an a, and also a following b'
    : /a[^bB]*$/i ?  'The string has an a, but not a following b'
    :                'String did not match'
    ;
[download]