"I did something bad, and I recognize that I did something bad, but there is nothing that can be done for it now, and there is technically no reason to apologize for that error, so let's just assume that I won't do it again, get over it, and move on with our lives."
Ruder than apologizing, but with the same meaning: a flippant apology.
"Er... my bad."
Persons of an older generation can find this quite annoying to hear when expecting an actual apology.
"Oh. My bad."
Used very commonly by gangsta-wannabes and other sorts of conforming posers, the terrible grammar tends to drive literate people up the wall in absolute irritation.
"Oh. Ha. My bad!"
"WHAT THE F?!?!"
Student: Sir I believe you are wrong. (student explains their answer)
Teacher: My Bad you were right and I was wrong, sorry for the misunderstanding