I had an interview, and I know I definitely could have done better. The company sent me the result thorugh e-mail, and as I expected, I did not get to the next round of interviews. Would it be so wrong if I reply this e-mail trying to point out how I would have improved? I would not give excuses, but recognize my mistakes and correct them somehow. I want to have another opportunity, perhaps not for this time, but later some other time. If it is wrong, then what could I say?
You could send them a thank you note like:
Thank you so much for interviewing me for the X position. I can see now that I should have done Y. I am still very much interested in working for your company, and will apply again in the future."
If they like what you write, they might reconsider, but don't expect it.
Would it be so wrong if I reply this e-mail trying to point out how I would have improved?
It's not wrong.
A politely worded Thank You letter, thanking the interviewers for their time and consideration, could also point out how you would have improved.
It's possible that it might help a small bit, but it's probably not going to make a difference. Most likely it won't hurt.