It was your problem, but not your fault

Didn't you just detect a hidden issue that might correct the format of the file? If you and the developer both fell into the same trap, likely other people will make the same mistake if you didn't detect the pitfall! Isn't a good QA's job to detect all types of issues? I would say that you did a great job finding this problem. So tell you findings to your direct manager and provide your analysis of why you and the developer both made the same mistake and provide a suggestion to the other team to better protect the format.

A few general tips to deal with mistakes at work:
1. never surprise your boss. So as you can see, replying to the other manager to admit that it was your fault would be a very bad idea. Not only does it contradict what your manager said, but it also surprises your manager.
2. think positive. Every one makes mistake, it's not a big deal. The important thing is to demonstrate what you gain from mistake, that shows your capability.
3. never admit your fault. well, it may not sound right, but if you think about mistakes you every made, there were always something that led you to the mistakes, right? Focus on the cause, not your error, unless you made a typo, then admit it and own it.:-)
I don't know if my suggestions fit your situation, but those are something I learned and I hope that they can be useful to other people.