How to answer an interview question

After working for my previous employer for almost 4 years, I was let go for what they deemed "poor customer service." I live in an at-will state, so they did not need to provide any specifics for why they were letting me go. Some of the examples they gave didn't match up to anything I could recall, and I found it rather interesting that the "errors" leading up to my dismissal started just prior to me going from night shift to day shift. I'm waiting for our state board to close out the file or whatever action they feel necessary on their end since both the facility and myself had to report the termination. My question is how, when I interview for another position, should I answer any questions dealing with why I left? Honestly, I was getting very frustrated with our management at the facility and I know that probably affected my work inadvertently, though I did my best not to let it. The only thing I can think of for a response is that I was frustrated with where I was in my career at that particular facility, and should have left before they had to take the steps they did. As far as what I learned, of course, is to recognize that degree of frustration whether professional or at an institutional level and to find someone to talk to first. If it doesn't improve within a certain timeline, say a month, then start looking for something else so I don't have to go down this road again. Any other suggestions from you all out there are appreciated. I realize I messed up and will do my best to not let it happen again. I just need help in knowing how to convey to a future employer that I am worthy of being given the chance to prove myself. Thanks for your help! :)