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It's nice that you care so much about patients. Unfortunately, bad outcomes happen regularly in our field when we deal with sick patients. Keep in mind "it's progress not perfection." To help you balance things out you should also try to come up with a list of patients/cases where you saved lives, especially when no-one else seemed to know what's going on. Lastly have compassion on yourself, no one is perfect and we all do the best with the limited information we often have.
Just knowing that you want to give the best care possible and recognize when things go wrong and could have been done better means you are on your way to becoming a great doctor. Many people think they are in the right at all times, but being aware of your own limitations is the first step towards improving. However, I would suggest that along with getting more experience and learning from senior doctors, you should also seek out patients whose outcome was positive so you can balance out your thinking.
I would first start with another residency that you matched into, then any research/abstracts/papers that you did. Then go back and talk about why you chose medicine even if it might be cliche. From there talk about the past clinical rotations and what did you like about them and what didn't you like about them, focusing on why anesthesia is for you. If time permits I would also go over some challenging patient encounters that you experienced and how you have been able to process them.
Often, I find that my instincts or intuition tells me some information is not right with certain patients, however, there are times I end up putting too much trust in the labs and imaging studies. I then feel frustrated when it turns out the investigations were the ones wrong. I need to learn to tune in more to my instincts.