Use a hash slice to build a lookup table:

use strict;
use warnings;

my @db = (1, 3, 5, 7, 9, 11);
my @in = (1, 2, 5, 8, 9, 10, 13);
my %lookup;
my @result;

@lookup{@in} = ();
foreach my $elem (@db) {
  push(@result, $elem) unless exists $lookup{$elem};
}

print "@result\n"; # should print 3 7 11.
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Of course, this doesn't actually remove the elements from @db. It creates a new array, @result, that holds only those elements of @db that were not also on @in. If your array is very, very large and you wish to avoid making a copy, this could be a problem.