You got the rejection email. Not the result you were hoping for. You are disappointed.
Take your time taking it in and getting over it.
Then, respond to the rejection.
More often than not, recruiters and hiring managers get the ‘silent treatment’ at this point. No response from the candidates.
Not responding to the rejection email is a mistake.
Remember that this is all about building a relationship. You were not the right fit for this position, but you may be for a different role in the future.
Instead of shutting the door on future opportunities (not responding to the rejection email), keep the door open. Send a nice email thanking them for taking the time to talk/meet with you. Reiterate what you liked about the company, and here I would especially talk more about the company, rather than the specific role, to open yourself up to future openings. You can add why you would be a good fit with their company culture, and that if a position that fits your skills and experience opens up in the future you would love to be considered for it.
This should be a short email. They are not going to read a long story.
Keep it professional. Show them that you can take a rejection, a set back, and that you can move forward in a positive manner.
The goal – leave a good taste in their mouth, ending this part of the interaction on a positive note, so that when a role opens up that fits your experience they will want to consider you again.