Regretful describes a person feeling regret — she was regretful about the decision. Regrettable describes the thing that causes regret — a regrettable decision. People are regretful; events are regrettable.
The core difference
One belongs to the person, the other to the thing.
- regretful — feeling regret: a regretful apology.
- regrettable — causing regret: a regrettable error.
The -able test
-able and -ible mark something as able to be or to cause — regrettable, lamentable, deplorable. -ful marks being full of a feeling — regretful, hopeful, remorseful. The suffix tells you where the feeling sits.
The construction to watch
"Regretfully, the event is cancelled" is a slip — the event is not doing the regretting. Regrettably is the adverb for the situation; regretfully describes how a person acts.