It was left at home by mistake/I left it at home by mistake. 'It was left at home' could mean you left it there on purpose.

"It was left at home" is grammatical, but it does not clearly mean you forgot it. I agree with Leigh that "It was left at home by mistake" or "I left it at home by mistake" clearly mean that you forgot. Another alternative could be, "I accidentally left it at home."