Jack was upset that in saving everyone and getting them back home things hadn't turned out so well not only for himself but the person in the casket.

Rose was cured from Cancer on the island but in going back home the cancer returned and killed her. Remember the funeral was in a black neighbourhood and the only black person we know Jack is really close to is Rose.

Ben also told Juliet that her sister had gone back into remission or something similar after being cured by the island and returning home.

Well that's my theory anyhow although the only odd thing is why nobdoy else turned up to the funeral, especially Bernard.