I only ever slapped mine two times when she was a child. Once when she ran out onto the road and once when she wrote on the furniture with an indelible felt tip pen. They were only brief slaps but I felt terrible. When she was about 15 she kicked me on the shin deliberately to see what would happen. I slapped her face so she decided not to do it again. For my part it was pure reaction because it was bloody sore.
I don't think you have anything to apologize for.
As for this teacher--I concur with those people who think this is wrong, but not a terribly big deal. Just tell the teacher to stop.
Children aren't made of porcelain. They're a lot harder to break than some people seem to think. And there are lots of cases of actual child abuse out there that need our attention.