可惜 + [clause]
[clause],(真 / 太) 可惜了
可惜的是 + [clause]
可惜 at the start of a clause means "unfortunately". It usually follows something good, then names what spoils it.
As a predicate, 可惜 is an adjective: 真可惜, 太可惜了, 很可惜. It sums up a whole situation.
可惜的是 is the written version of the opening, with the regret named first.
It also covers waste: throwing away good food, or a talent not used.
可惜 describes the situation, not the person. 我很可惜 doesn't mean "I'm sorry" or "I feel bad"; put 可惜 on the situation.