'11, 22, 33, 44, 55' is a string (not an array), so
$INPUT{'checked_ids'} =~ /^(?:\s*[0-9]+\s*,)\s*[0-9]+\s*$/
will do what you want.

Once validated (as shown above), you can convert the list to an array as follows:
@checked_ids = $INPUT{'checked_ids'} =~ /(\d+)/g

If you really did need to check an array:

my $bad;
foreach (@array) {
   unless (/regexp/) {
     $bad = 1;
     last;
   }
}

die("Naughty\n")
   if $bad;
[download]

or

my $num_bad = grep { !/regexp/ } @array;

die("$num_bad naughties\n")
   if $num_bad;
[download]