You could do this with a global match but it probably fails your "just gets ugly" criterion.

use strict;
use warnings;

my $str = q{"one","two", "not three" , ' four',"five " };

my @arr = $str =~ m
   {(?x)
       (?<=['"])
       ([^,'"]+)
       (?=['"])
   }g;

print qq{-->$_<--\n} for @arr;
[download]

Here's the output.

-->one<--
-->two<--
-->not three<--
--> four<--
-->five <--
[download]

This method is going to fall down pretty quickly as your data gets more complex and I agree with others who have suggested some sort of CSV module to tackle the problem.

Cheers,

JohnGG