If you have another interview and aren’t successful, don’t be afraid to write a nice, polite email or letter asking for some feedback. The worst they can do is say no!
I think the example Glenys gave is very helpful, and something along those lines should be fine.
Don’t come across as looking for sympathy or begging for them to give you another chance.
Thank them for the opportunity they gave you, and ask for “brief feedback” to help you improve for next time.