Sometimes it is a blessing in disguise, but go ahead and share it publicly if you wish, especially if you were fired for reasons unjustified but there is also the chance that the startup simply let go of the people they thought were the least valuable asset to their company. Similar situation happened to me.
I say it might be a blessing in disguise because... I worked for a software company that designed kiosks for solar panels and I worked on the design of the software, how it looked, special requests, etc. Anyways, in the interview, they said they were hiring me to help catch them up.. they had about 150 clients they had to cold call to get information from them, assets, etc. -- these clients had already paid their money, but hadn't received kiosks or software. Anyways, to make a long story short, about a year later, I had knocked them down to about 30 clients left.
Meanwhile, our competition was also growing, and these companies were developing in HTML5, whereas we were still building in flash-based software, with an in-house developer working on it upgrading us, but the actual update never seemed to come. Anyways, it seemed that because that company refused to update their software, we lost out to our competition, or we were starting to lose.
I was called into an office, where human resources told me they had to let me go. So they gave me the choice: If I didn't file for unemployment, they would give me a 3-week severance pay. Fortunately for me, I was working a second job, so I actually couldn't file for unemployment, so that helped me out and was like getting paid for doing nothing for 3 weeks. Awesome how some things worked out, though in the first week was rough, I was certainly devastated.. nothing can prepare you for the moment you get laid off... and you go over so many scenarios in your head, "What did I do wrong? What could I have done better? What email did I forget to send? What assignment did I miss? Was it that one time I was 10 minutes late coming back from lunch? Was it that one day that I was running late to work because I overslept?" You go over everything because honestly, you just don't really know.
I had later found out they were struggling badly, financially, and I was the most expendable, so they let me go. I was lucky because I also kept in touch with my former co-workers, who all were not being paid on time, who were still showing up to work, not knowing if they were going to get paid or not, and some of them had to take the company to smalls claims court to get what they were owed. The company soon went under and I think they managed to stay in business by keeping three employees, simply for maintenance issues for existing clients.
So lucky to be let go first.. as everyone else would soon have to struggle, whereas I had a nice free ride for 3 weeks of making money by doing nothing, but accepting the fact that they laid me off. Did I write about this company? Sure did but there was and is still no reason to mention their name or be mad at them. Tough world of competition out there and they lost. Do I expect anything from it? Absolutely not. Life goes on and you find other companies.
Startups are either successful.. or they aren't. And I am sure no startup wants to fire or lay off their employees, but sometimes, the startup is just failing, and they feel horrible themselves, wanting to have been successful, but realizing the reality of the situation.
Life goes on.. the second job I was working at the time.. became my primary job, and I still hold the position over 4 years later, as a very satisfied employee who loves his job. Look to it as a learning process, an experience, and keep moving on til you find the job or come up with your own that will set you up for however long you need.