Yes, please own your mistake. A no-blame culture doesn't mean you can't take responsibility for your own mistakes.
I work for a company which also has a "no-blame" culture. This implies that if something bad happens, the first thing we do is "mitigate the effects". Then we fix the cause. And afterwards, we write a document explaining what went wrong, how did we notice it went wrong, which steps were taken, and offer suggestions how to avoid that in the future. And we make this document available to everyone (we've an internal website to search those documents).
But while we don't blame (notice that all steps describe above are focused on "what happened" not on "who's responsible"), we still value owning up to mistakes. The person who made the mistake is going to be one of the more valuable people to fix it -- they're the one most familiar with the code. Owning but not blaming also helps in getting bugs fixed as soon as possible.
Of course, that doesn't imply you need to make a big show out of it. Just say "I made a mistake. I'm working on a fix right now".