Why can you not use @Inject in POJOs instantiated with new

Issue

I have @Stateless object which I would like to inject:

@Stateless
public class MyEJB {
    public String myMethod(){
        String res = "myMethod";
        System.out.println(res);
        return res;
    }
}

When I try to inject it into a POJO, it does not work and is null.

public class MyPojo {
    @Inject MyEJB myEjb;

    public String myPojoMethod(){
        String res = "myPojoMethod .. ejb = " + myEjb;
        System.out.println(res);
        return res;
    }
}

Why? I do not think that Java EE spec puts any requirements on lifecycle of objects that use @Inject?