Is it rude to send a self-correction followup email to professor?
Different cultures have different standards of politeness. Educated people tend to understand that. By UK standards you were more polite than you needed to be, but by Japanese standards, perhaps, just right. 

Don't think of it as a mistake. There should be no issue at all. In fact, I'll guess you've made a good impression. 

The opposite problem, in which a person isn't polite enough in the local culture is a bit more of a problem, of course. I hope that if I were to meet you in Japan, you would forgive me for my seeming lack of politeness in some situations imagining (correctly, I hope) that it isn't intended.