You forgot to remove the \n character when they submitting the value to STDIN. Try this,

open(INPUT, "hosts.txt") || die "Error opening 'hosts.txt'\n";
my @hosts = <INPUT>;
while (<STDIN>)
     {
     chomp($_);
     foreach $host (@hosts)
         {
         if ($host =~ m/^$_/)
             {
             print "Host found: '$host'\n";
             }
         }
     }
[download]

As someone pointed out, the foreach should not be used with the STDIN and the brackets around @allhosts was wrong too. Fixed.