How should a teaching assistant explain his absence to the course instructor? As an international TA getting accustomed to the landscape of my University, I managed to earn the ire of my instructor/professor for having not shown up during the discussion/office hours. 

In a strongly worded mail, he has sought an explanation while reprimanding me saying that another instance of this would lead to serious consequences.

I am afraid that I may lose my assistantship as I curse my folly for being so careless. I have apologized to the Professor over mail but from the tone of his reply, he seems to have not considered it. Please suggest how I must handle this predicament.
The best way to handle this is to acknowledge that you've screwed up, and to explain how you're going to make sure that you won't miss any class meetings and other events in the future. If there's a justification for why you missed the event (for instance, if you had an examination for a class you were enrolled in overlapping with office hours), you can mention that.