This is probably the reason that "I'm sorry for your loss" has become the default when talking to someone whose loved one has died. The problem with that is that it's already become a cliched phrase, so it sounds insincere. I actually say things like "I'm apologetic" when that's what I mean, and I sometimes use "regretful" or "chagrined" when I mean those. English is full of words for these nuances, but they don't sound conversational.