It's a pity isn't quite worn out yet, but using Pity! as a complete sentence is distinctively "Britishy". What is old-fashioned is to use the 'tis contraction instead of it is: `tis a pity!
The word pity is both a verb and noun. Should the public pity Lance Armstrong? It is an important word in the English language for which there is no equally glib substitute. Feel sorry for is three words which can be expressed by one.
In North America, the expression too bad is often used rather than it's a pity. For instance, rather than it's a pity you aren't able to attend becomes too bad you aren't able to attend. Not all uses of one phrase substitute for the other. Too bad! by itself also means although you don't like it, you should stop complaining and accept the situation (also expressed by phrases like tough luck!, suck it up! or deal with it!) whereas it's a pity has no such use.
It's a pity (that I don't know how to get to the airport) isn't a usage you will likely hear from a native speakers because it expresses an irrational degree of regret over something trivial. It sounds as if the speaker missed some past opportunity to learn how to get to the airport, and for some reason it is regretfully too late to acquire that knowledge.
The "Britishy" Pity!, however, can be used for lamenting trivial annoyances, similarly to words like darn, shucks, drats and so on.
A: I'm afraid we're out of tea, darling.