You're correct in saying that even if you've been wronged, you shouldn't badmouth your former manager(s). You're also correct in predicting that an interviewer will ask questions about why you left and why you don't want your former employer used as a reference.
What you're incorrect about is that you can't tell the interviewer why you were terminated. Look at the questions that you envisioned the interviewer asking: They're not only the obvious questions, they're also reasonable ones. And not getting a satisfactory answer – that is, not getting the truth, combined with not getting a reference – will make it extremely unlikely that the interviewer will recommend you for hire.
The most important thing is to be honest. Give a balanced account of the circumstances, and while it's fine to say that you disagree with the reasons that resulted in your termination, don't be accusatory (the badmouthing part) and don't make excuses. Whether you agree or not, illustrate how you are working to improve those issues that were said to be the cause of your being fired, for example, that you are working on time management or improving your communication skills. Keep the explanation brief. (You may want to see our previous items: Being fired can be a major blow to your confidence, but it's not the end of the world, so don't sabotage yourself with dishonesty.