Here is code that parses your data format and flags sequences that are unique in your data. The  %count hash can also be used to process duplicates.

#!/usr/bin/perl -w
use strict;

my (%count, %ann);
while (my $line = <DATA>) {
   chomp $line;
   if ($line =~ /^>atc:(\S+)\s+(\w+)$/)   {
      $count{$2}++;
      $ann{$2} = $1;
   }
}

foreach my $seq (keys %count) {
   print "Unique seq $seq has ann $ann{$seq}\n" if $count{$seq} == 1;
}

__DATA__
>atc:AGR_pTi_39_1-45_FD cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
>atc:AGR_pTi_47_1-45_FD ccttacaggtcattgagcacagaggaatgttcaatttagggaaac
>atc:AGR_pTi_39_1-45_F      cctttcaagtcatagaacaccggggcatgtacaacttgggga
+agg
>atc:AGR_pTi_47_1-45_F      ccttacaggtcattgagcacagaggaatgttcaatttaggga
+aac
>atc:AGR_pTi_39_1-45_RD cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
>atc:AGR_pTi_47_1-45_RD ccttacaggtcattgagcacagaggaatgttcaatttagggaaac
>atc:AGR_pTi_39_1-45_R  cctttcaagtcatagaacaccggggcatgtacaacttggggaagg
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