You have to provide us with line numbers. This can't be done on perlmonks. You can get them with:

perl -pe '$_="$.: $_"' your_input > your_output
[download]

I'm not sure how your desired output should look like. Maybe this will help you. It uses RegEx:

use strict;
use warnings;

while (<DATA>) {
  my (@fields)= split /, /;
  foreach (@fields) {
    if (s/^"((?:[^"\\]|\\.)*)"$/$1/) {
      #correct
      tr/\\//d; # No more \
      print "$_\n";
    }
  }
}
__END__
"Perlmonks", "http://www.perlmonks.org", "excellent ;)"
"csv", "csv\"xxx", "trall\ala"
[download]

Short explanation for the RegEx:

/^"((?:[^"\\]|\\.)*)"$/$1/

^"

matches your field's quotechar at the start of the field

(...)

will "remember" what was matched inside the quotes

(?:...)*

This will match anything in place of the ... and tells the parser that it may apear as often as possible. Even zero times

[^"\\]

will match any character but " and \

|

is an alternative. Either the left or the right part has to match

\\.

Will match any "escaped" character

"$

again your quotechar but now at the end

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