@karadayi
There are two PageSpeed "modules": one for Apache and one for Nginx (which requires a custom build of Nginx).
Both PageSpeed "modules" are experimental, so there is a reason for your hoster and Plesk to not support these "modules".
However, the good news is that you can use default Nginx, as shipped with Plesk, to configure almost all (valuable) options of the PageSpeed "modules".
In general, it is a good idea to have a Nginx proxy in front of the Apache web server, to reduce the load on Apache.
From that perspective, it also is a good idea to setup specific Nginx directives that allow you to enhance performance, in a similar way like the (Nginx) PageSpeed module does.
Also note that using "bare" Nginx directives (as opposed to using any of the two PageSpeed modules) is not associated with the performance penalty, that is commonly encountered when using one of the PageSpeed modules (note that the PageSpeed modules can really drain the server´s resources).
Hope the above explains a bit of the background.
Regards......