I'm really sorry you did not get a return offer. This is really hard.
Remember, the greatest accomplishments come from temporary defeat. Do not let this bring you down - keep pushing for the next offer.
At the same time, reflect. You're “blaming” the staffing and project lead, but not yourself. In consulting you are going to get bad projects, bad clients, bad managers.
If you don't reflect on what you could have done better, if you don't attempt to change, and if you don't recognize that this problem will follow you in any consulting role, you will continue to not get offers/promotions.
For context, I had a really similar internship (tough project, a boss I really didn't gel with), but I found a way to make it work (buried my head, played the game, etc.). I got the return offer.
Now, that's water under the bridge but please make sure to learn/adjust/adapt to see how you can navigate the next tough situation WHEN it happens.
The good news is you should be just fine on future interviews :)
An internship is just that - an internship! If they do happen to bring it up, you can just say that it was a great experience, you learned a lot, it re-asserted your interest in consulting, but that you're looking to work full-time in a different country and therefore interviewing!