Another method by which people appear to apologize without actually doing so is to say Im sorry youre upset; this suggests that you are somehow at fault for allowing yourself to get upset by what the other person has done.
主干：Another method...is to say...; this suggests that...
本句是由分号间隔的两个分句构成的并列句。前一分句中，by which引导定语从句，修饰主语another method，不定式to say作表语，引号里的直接引语作say的宾语。后一分句中，that引导的从句作suggests的宾语。
译文：另外一种表面上看似乎是在道歉，而实际上并没有道歉的做法是说你感到委屈，我很抱歉，这表明，如果因为别人所做的事情而让你自己感到委屈的话，那么你多多少少是有过错的。