How to use DI with simple objects? I have a simple class to which I am providing some values via constructor and I would like to use DI. This class has no relation to Drupal(not a plugin, form, entity,...).

It serves as a wrapper for dataset where I need to do some data manipulation by using few services.

I wanted to use the ContainerInjectionInterface but it only has the create() method and it does not look like it can be used for this purpose.

Can the DI in D8 even be used for this purpose?
Yes. Just require the services you need in your constructor, and wherever you create your object, pass them in.

That is the very definition of dependency injection.

The container/services are just a way to describe your dependencies to the environment/Drupal so it can do that automatically but that is in no way a requirement.

What you probably want to do is to use the factory pattern, so that you have a factory, which you can define a service, which offers a method to get your value object with the necessary services injected. Drupal 8 has various examples for the, for example KeyValueDatabaseFactory (keyvalue.database), which has a get($collection) method. Each call creates a new object, passes the dependencies that object needs to it and then returns it.