Manager not accept my resignation notice

Hello everyone, need your advice.

I got a job offer that commence on for example, 1/15. I communicated to my manager that I would resign in 2 week but I miscalculated the date. For example 1/1 notice -> last day would be 1/15.

I stupidly put my last date as 1/14 (to begin work at new company on 1/15)

Now my manager said that he will not let me go because the company rule for resignation notice is 1 month. And because of my stupid mistake I cannot use the Japanese labour law of 2 weeks notice either..

What should I do now?