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

my $string = 'foo "A small \"dog\" eats pie." bar "foobar"';

print $1 while $string =~ /(?<!\\)"(.*?)(?<!\\)"/gs;
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Addendum:

Hmm. It didn't take me fifteen minutes to write this post. perlmonkey must be typing at relativistic speeds. btw--double quotes are not special in a regex; you don't need to backslash them.