I'm not like on my knees begging for forgiveness, but I feel regret that an unfortunate thing happened. To me it's a similar situation to if I, say, accidental

I'm not like on my knees begging for forgiveness, but I feel regret that an unfortunate thing happened. To me it's a similar situation to if I, say, accidentally spilled your drink; something of that nature. (I guess different people could attach different amounts of significance to the word. To me it simply means, "I feel sympathy that this unfortunate thing happened, and I wish it had not.")