That's a shame is an expression of mild sympathy at bad news. Oh, that's a shame.
It is the standard British response to a small disappointment, and it does not fit a real tragedy. Shame here means a pity rather than anything to do with disgrace.
1phrasethat's a shameAn expression of mild sympathy at bad news.
“He said that's a shame and offered to come another day.”
that's a shame is a phrase.
Practised in Small Talk & Everyday Phrases