Thank you for your response, however, I've finally managed to make it work myself. For all those who might have similar issues this solution worked for me:
I created a subdomain 'tasklist.aportsupport.cz' which has its own root folder on my shared host. In this folder I put all Zend folders with their default structure. Also I created index.php file in which I wrote this:
<?php include 'public/index.php';
This index.php is located in root of tasklist.aportsupport.cz with default Zend Framewrok .htaccess in which I added this line:
RewriteBase /
Also all CSS, JS, imgs etc. files are located in that root folder. Everything works just fine!