Should I use global variables?

I have been reading about global variables and how bad they are but I am stuck in one place due to that. I am going to be very specific about if I should use global variables in this scenario.

I am working on a game engine. And my engine consists of lots of managers. Managers do certain tasks - they store resources, load them, update them etc.

I have made all my managers a singleton because so many classes and functions needs access to them. I was thinking of removing the singleton but I don't know how i can not have it and get access to these managers.

Here is an example of what I am trying to tell (im bad at english, sorry):

Singleton.h

template<class T> class Singleton {
private:
    Singleton( const Singleton& );
    const Singleton& operator=( const Singleton& );

protected:
    Singleton() { instance = static_cast<T*>(this); }
    virtual ~Singleton() {}

protected:
    static T * instance;

public:
    static T &Instance() {
        return *instance;
    }

};

ScriptManager.h

class ScriptManager : public Singleton<ScriptManager> {
public:
    virtual void runLine(const String &line)=0;
    virtual void runFile(const String &file)=0;
};

PythonScriptManager.cpp

class PythonScriptManager : public ScriptManager {
public:
    PythonScriptManager() { Py_Initialize(); }
    ~PythonScriptManager() { Py_Finalize(); }

    void runFile(const String &file) {
        FILE * fp = fopen(file.c_str(), "r");
        PyRun_SimpleFile(fp, file.c_str());
        fclose(fp);
        fp=0;
    }

    void runLine(const String &line) {
        PyRun_SimpleString(line.c_str());   
    }

};

Entity ScriptComponent

#include <CoreIncludes.h>
#include <ScriptManager.h>
#include <ScriptComponent.h>

void update() {

    ScriptManager::Instance().runFile("test_script.script");
    //i know its not a good idea to open the stream on every frame but thats not the main concern right now.
}

Application

int main(int argc, const char * argv) {
    Application * app = new Application(argc, argv);
    ScriptManager * script_manager = new PythonScriptManager;
    //all other managers

    return app->run();
}

As you see I am not even including the files above in my ScriptComponent.cpp file which wins me some compilation time. How can I get that kind of a result without globals which will make it easy to integrate as this one. The singleton is not thread safe but adding threads won't take a long time.

I hope I could explain the problem.

Thanks in advance,
Gasim Gasimzada