my $sendmail = "/usr/sbin/sendmail";
open (MAIL, $sendmail) or die "cannot open sendmail";

You open sendmail for reading, which succeeds. The prints, however, do not succeed. It's not common to do, but you could write:

print MAIL "To: Adminmail\n" or die $!;
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to find that out (I hate it, but when debugging, it can really aid)

Instead, you will have to open sendmail as a write-only pipe.

open MAIL, "| $sendmail" or die $!;
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or, better yet: (Perl 5.6+)

open MAIL, '|', $sendmail or die $!;
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Sendmail expects the to-address on the command line, so it will still not work. You do NOT want that, so you're going to avoid it by putting "-t" on the command line instead. While you're at it, add "-oi" too, to avoid having to end with a single dot on a line.

my $sendmail = '/usr/sbin/sendmail -t -oi';
open MAIL, '|', $sendmail or die $!;
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Of course, best is to use one of the many existing mailing modules instead.

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