If you want to substitute at the same time as the matching, the following may work for you:

#!/usr/bin/perl
use strict; 

my $string = "CATINTHEHATWITHABAT";
my $regex = '\wAT';
my @matches = ();

while ($string =~ s/($regex)/lc($1)/e){
    my $match = $1;
    my $length = length($&);
    my $pos = length($`);
    my $start = $pos + 1;
    my $end = $pos + $length;
    my $hitpos = "$start-$end";
    push @matches, "$match found at $hitpos ";
}

print "$_\n" foreach @matches;
print "$string\n";
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I've used the e modifier (see perlretut) to evaluate the lower-case transliteration of the matched string.

Caveat: This becomes an infinite loop if you use the i modifier, since you will continuously overwrite the first occurrence of 'cat'. If need case insensitivity, perhaps you'd want my $regex = '[A-Z][aA][tT]|[a-z][aA]T|[a-z]At'; or equivalent for your real case.