I don't usually consider myself qualified to give out perl advice, and after reading your post again I realized you question was why doesn't your code work, and not asking for alternatives. Still, others already responded to that so I'll just offer my alternative using regex:

 while (glob '*.pkl') {print qq(Found $1 in $_\n) if /(A[1-9])/}
[download]

Do you need it to print which alphanumeric signatures it didn't find? This could be easily added, but it would compromise the cute one-liner aspect. ;-)