I just had my HEC Paris, ESCP and EM Lyon interview for the same Master's and I also feel like I bombed it, but don't get down too much on yourself. These can be a great learning experience and I can guarantee that next time you find yourself under these circumstances, it'll go much better. I bet that right after the interview you not only knew it didn't go so well, but you also knew the different ways in which you could have answered these questions. Sounds like it wasn't technical at all, which means it was just nerves and as much as you won't get another chance at this exact interview, it won't be the last one in your life and that's the beautiful part of failing. Everytime you make a mistake it's a chance to get stronger in whichever way that you came up short.
Interviews for graduate schools are not unconventional at all, and the earlier you become comfortable in that setting, the better. Most of the top programs in any field, not to mention all top MBA programs, have this component. What helped me is to continually realize that this is a chance for me to differentiate myself from the crowd and sell my candidacy. Don't treat it as a burden or an interrogation process but rather a way to instill confidence in the commission that you are the right candidate.