What is appropriate (both honest and best for the interview) depend heavily on a large number of details.
Based on what you've described to me, if I were interviewing you the things I would need to know to decide if I'm going to consider you are...
Was it a mistake?
We all make choices based on the available data, if we are doing what logically the data points to then if it doesn't work out it's not really a mistake, it's the best choice we had based on the data that happened to not work out.
When you made this choice that didn't work out
- Did you have sufficient data to act in an informed manner?
- If not, was this a situation that needed immediate action, or could action have been delayed?
- If so did you follow what made sense based on your data, or go against what that data implied.
What I'm trying to establish here is was your mistake the decision itself, or your approach to the decision. One is just unfortunately the way things worked out, the other is a mistake.
Neither is "good" but one I would easily let slide as a one off, the other though would be a solid ding against you. (not that it would prevent me from hiring you entirely, just it would mean you'd need to have something to make up for the ding)
The next question comes to play in leadership of your intern. You made a choice that didn't work out or a mistake, either way these things happen, we're all human.
Where did things go wrong with the intern?
This is very important to me even more so than the choice itself, the choice is potentially a one off, failure in leadership on top of that could be a deal breaker.
How long after you made the erroneous choice was the error known?
Immediately, a few minutes, a few hours, days?
You mention the intern had time to repeat this problem 77 times. This could happen within fractions of a seconds all the way to over the course of months.
The two big questions I have here are:
- Did you take the time to see the results of your actions before the intern was cut loose to repeat them?
- Once the problem was discovered how long was the intern repeating the issue until stopped?
If the windows were tight and everything looked on the up and up I wouldn't hold it against you, it'd fall into the one off snowballing, which is unfortunate, but not a big deal.
If you never confirmed things were in order before cutting the intern loose, or there was a large window between discovery of the problem and putting a stop to the intern's repeating it that's a real big concern, and one that could potentially get you pulled from consideration.
The next question is did you know the intern was doing this? Basically to me it's only an issue from the moment it became known to the moment it was put to a stop, or if the window was simply too big.
What should you say?
This depends on the nature of the company and the details.
I would need a number of things from you. First you need to fully shoulder the blame, the only way the intern catches blame in my book is if they acted against your guidance. (Doesn't appear to be the case here)
Now shouldering the blame is a plus in my book, it means you take responsibility of your actions which is important, no one likes the guy who deflects blame on others.
Honestly if you have a decent work history, top performer, etc. Even if this was a legitimate mistake you made an assumption, things derailed, and while you started trying to put together the pieces your guidance of the intern went down the tubes I can actually forgive all that.
So long as you take ownership of your actions both good and bad, and you are able to convince me this will never happen again.
Will this get you the job? Not necessarily, but it won't cost you the job either, all depends on who you're up against. The way this will cost you any hope with me is if you seem to be blaming others, or if I feel the mistakes made will be repeated.