Expose a Singleton to other classes using an interface

I'm making a game in Unity C# using a Singleton GameManager and I was warned that using references of the class in other scripts like GameManager.instance.someVar makes the code fragile and difficult for later edit. So I looked for how to access a singleton with interfaces but haven't found what I was after. As I wish to code properly, I would like someone to point me to a decent source that tells me how to do so, or have him/her tell me in brief.