I don't think that your code does quite what the OP wanted. The contents of the wanted array as posted indicate that the single- and double-quotes should be preserved around the text they are quoting. This could be achieved using a capture in the regex used to split the string.

#!/usr/bin/perl -l
#
use strict;
use warnings;

my $str =
   q{jfjsa as,.n d"fdsafjl"jop'fdsjklf fds'457"fjdsklaoir"jkl45;fs ier
+987543" fsdjkal"};

my $rxSplit = qr
   {(?x)                     # Use extended syntax
       (                     # Open capture group
       (?:                   # Open group for alternation of
       "[^"']*"              # "whatever"
       |                     # or
       '[^"']*'              # 'some other thing'
       )                     # Close alternation group
       )                     # Close capture group
   };

my @arr = split m{$rxSplit}, $str;
print for @arr;
[download]

The output.

jfjsa as,.n d
"fdsafjl"
jop
'fdsjklf fds'
457
"fjdsklaoir"
jkl45;fs ier987543
" fsdjkal"
[download]

I hope this is of interest.