Is the following code what you're looking for ?

use strict;

my @array = qw (bga);
my @new_array = qw (bga cbga test);
my @tester;

print "@array\n";

# 
#foreach my $temp(@array) {
#    chomp($temp);
#    @tester = grep !/^$temp$/ig,@new_array;
#}

my $temp='('.(join'|',@array).')';
@tester = grep !/^$temp$/ig,@new_array;


print "@tester\n";
[download]

UPDATE :
Ooops davorg said it faster...
Furthermore if it's case-sensitive 'ne' is better than the regex used in my examples...

UPDATE2 :
Thanks Davorg for catching my error !
Only the last element of array will be taken out of the list,
as the @tester array is completly reconstructed at each step of the loop (only ok with one element ;-)
I've corrected the code with another solution...
But you'd definitly better use davorg's one.

"Only Bad Coders Code Badly In Perl" (OBC2BIP)