If your private function is not in the same class as your click event handler, you can't do it... that is because private functions are
private to their class. So let's say you have the following:
Module MainFunctions
Private Sub MySub()
End Sub
End Module
And from within default.aspx you try call MySub() it will not work because MySub is declared as private and you are making the call from within the default.aspx class. (There is a class behind that page... that is the code-behind where you are finding the button1_Click event handler.)
If you want to be able to call MySub from within the event handler, MySub either needs to be Public or Friend. (I suggest Friend) This is true for functions and subs in either a module (which is a static class in VB) or a regular class. Of course, for a class you have to create an instance of the class before you can call the method:
Dim myClass as new MyClass
myClass.MySub()