I was fired from my last job for making the same mistake to many times after 22 months.... I need help with how to address this in interviews

So, to make a lot of details precise, I held my last job for nearly two years before getting written up too many times for mislabeling test samples. I won't make excuses for this, especially since "attention to detail" is a key required skill in my work field, but constant changing of job demands and rushing to complete quotas led to mistakes. I'm in desperate need of advice on how to handle getting asked the inevitable "why are you looking for work?". The company's HR has told me their policy is to only disclose employment time and position held to prospective employers, but I can't rely on this being to my favor, nor can I reliably get away with saying I'm still employed and simply looking. Moreover, I'm worried about how being out of a job after being with the company for a while will look. I don't want to say I was laid off, and I simply cannot think of any ways to spin my circumstances in a positive direction, or any good reasons to give in its place that don't mention how I lost my job over performance after nearly two years. Please help, I'm a loyal and diligent worker who wants to succeed, and I'm getting nervous about bills and how a long unemployment will affect my career.