"I let down myself." sounds very awkward and unnatural. "Myself" should come between "let" and "down". :)

I let myself down

Hello Susana, 'let down' is a phrasal verb and generally if you have a pronoun - (a word to replace a noun) it goes between the verb and the preposition. I have a video about phrasal verbs you may find useful https://www.youtube.com/watch?v=2UVgTCILUbs&list=PLIcNItpI5Y7CByenUL965_JYRKIeFp0Ch&index=3 Best wishes Bob

It's always 'I let myself down'.

You would say "I let myself down".