Did you use multiple logistic regression to do this?

Most people will say that with only 11 events, your sample size may only support 1 predictor at most. How many predictors did you examine and how were they formatted (e.g., binary variables), and did you test them one at a time? A p-value > 0.5 for an AUC value just means the variable is not any better then chance, and since they were close to 0.5, that doesn't bode well for it just being a small sample size thing.

Since your outcome was death status, was it not feasible to examine data with survival model which would take into account time?

A post hoc sample size / power calculation could be frown upon, if it directs you to collect more data to just try and get significance.

If variables are truly independent and you are not looking to increase sample size or kept the study going, you could easily get an idea of power issues by just calculating it for bivariate fisher test power analyses (if IVs are categorical), since you have a finite sample size. So run a power analysis for Fisher exact test for a outcome and variable.

Another option would be to run simulations to determine what sample size would be need for distinguishing say an AUC value of 0.55 from 0.50.