If the manager asks you if you did well on that job, the manager is asking you for your input. When you say "The job didn't go 100% well. How can I avoid rating on myself", it looks like you want the manager to ask for your input only when things go 100% your way and the manager has nothing but nice things to say about you.
I am blunt. I am not afraid to say that I screwed up if it's indeed the case that I screwed up. I will tell my manager that I screwed up even if I were 10% responsible for a situation but if I had taken some extraordinary step such as taking - no, yanking - ownership of a task that a colleague was failing on would have changed the outcome. My managers appreciate my clear thinking, my unadorned opinion and my sound judgment, even if they don't appreciate from time to time that I am not high on tact. They don't have to like everything I say and in fact they don't. But I believe that my feedback keeps them grounded in reality and keep them away from any notions of wishful thinking. And it's important to them that their assumptions and presumptions are grounded in reality, because that's the basis for sound judgment and sound judgment is the basis for sound decisions. Neither weak and insecure managers nor weak, insecure professionals have any business being in the workplace.
I have found appraisals a useful examination for self-examination, a welcome forum for how the management sees me and conversely, how I see the management. I have had Alice-in-Wonderland appraisals that caused me to lose confidence in the intellectual honesty and judgment of my managers and motivated me to seek work elsewhere. I do not willingly continue to work for someone I don't trust, because I think it's bad karma and there is no good outcome from bad karma. Appraisals is a two-way street: they appraise me and I appraise them. And we have a right as well as a responsibility to each other to appraise each other.
Appraisals are a snapshot of what you are doing, and where you are going. If used as intended, they are a terrifically useful feedback mechanism for the appraisee as well as the appraisers. One key question that I have for my managers since I have a captive audience is "What is it that you'd like me to do for you and that you know I can do for you that I haven't been doing for you?"
You seem to see appraisals as either some kind of "how great you are" praise session or some kind of blame game session. I suggest that you disabuse yourself of that notion. If they had wanted to fire you for whatever reason, they would would have fired you without waiting for a formal appraisal to take place.