A gracious reply is the one people remember, and it is the best chance of useful feedback. Fill in the boxes and the email writes itself.
Filled in with an example. Type in the boxes to make it yours.
Subject: Re: Senior Analyst
Hi Tom,
Thank you for letting me know, and for the time you and the team gave me through the process.
I would really value any feedback on what would have made my application stronger. Even a line or two would help me with the next one.
I enjoyed meeting you and would be glad to be considered for future roles.
Kind regards,
Sam Hollis
Reply within a day, and ask for feedback on what would have made you stronger, not why you missed out. Many employers will not give detailed feedback, so do not push if they decline.
If they do reply, thank them, and use it on the next application.
More on this: Reapplying to a company that rejected you
Keep every letter with the job it belongs to: jobtracker.co.nz is free while you're between jobs. See all the letter templates.