UPDATE: whoops a closer inspection reveals this doesnt match your output requirements, but i leave it here as it is a useful technique.

This is a situation where For some problems like this m//g in scalar context comes in useful:

sub append_n
{
      my ( $str, $array ) = @_;
      my $nstring = "N" x length($str);
      pos($str)=0;  # reset the search position on $str
      foreach my $sbstr ( @$array )
      {
        $str=~/$sbstr/g and
            substr ($nstring, $-[0], length($sbstr)) = $sbstr
      }   
      return $nstring;
}
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Outputs (when combined with a modified version of your code)

m//g: GATTACGNNNNGCGCTCGNNNAACGGCA
Orig: GATTACGNNNNGCGCTCGNNNAACGGCA

m//g: GATTACGNNNNNNNNNCGTGTAANNNNN
Orig: GATTACGAGNNNNNNNCGTGTAANNNNN

m//g: NNNTACGAGTNNNGCTCGTGNNNNNNNN
Orig: NNNTACGAGTGGCGCTCGTGNNNNNNNN

m//g: NNNNNNNNNNGGNNNNNNNNNNNNGGNN
Orig: NNNNNNNNNNGGNNNNNNNNNNNNNNNN
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