How about something like this:

#!/usr/bin/perl
use warnings;
use 5.12.4;

my $string = "NNNNNCATTCCATTCATTAATTAATTAATGAATGAATGNNNNN";

while (<DATA>) {
    next if /^>.+/;
    next if /^$/;
    chomp;
    $_ .= $string unless eof;
    print;
}
__DATA__
>contig number 11
tttgctcggaggggatc

>contig number 23
gaaaacacttccttattatacaggtaaaccgtatttggat

>contig number 3
aaagctcggaggggatcccct

##########
It prints:
tttgctcggaggggatcNNNNNCATTCCATTCATTAATTAATTAATGAATGAATGNNNNNgaaaacactt
+ccttattatacaggtaaaccgtatttggatNNNNNCATTCCATTCATTAATTAATTAATGAATGAATGN
+NNNNaaagctcggaggggatcccct
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