Yesterday I asked for leave on 14 and 15 day, but I was wrong and I need another 16 day. How to apologize and ask for more vacation?
The phrasing you've already used in your question would be good enough. The only real error I can spot would be that "14 and 15 day" would be referred to as "the 14th and 15th". You should also mention the month if it's not already clear which month you're referring to.
I know I asked yesterday for the 14th and 15th off work and I'm really sorry but I made a mistake and I need the 16th off too. Could I please take that day off as well?