Sorry man, my bad.
Think about it, the perfect excuse, or need to apologise. 'Sorry' the best word for an apology, condones guilt, and remorse. As if to say, I really wish that didn't happen, won't happen again.
Addressing the person as 'Man.' That's what you call you friends, right?... "Hey man... lets go to the game"... it almost assumes the person is already your friend and face it, its hard to stay mad at a friend.
Again, to end the statement, you again admit guilt, as a sort of 'no contest' in court. No fighting, no need to show evidence, its clearly my fault.
ex: Man, those were the answers to the Chemistry exam you gave me, I needed the answers to the Bar exam...
"Sorry man, my bad."