It doesn't translate into English ;) There're some mixed feelings we share in it, they are your unspoken wish for something, slight sadness resulted from the *unattainable* wish. For example, you hung out with your friend that you haven't seen for ages. A day was too short for you, there's much to talk about and to do with him/her. So seeing off your friend, you wish you could have a few more days or even just a single day to spend with her/him. I felt 아쉽다 when Korea was defeated by Uruguay 1-2. =3

yes it could be... ,but it depends on context. I think it is one of most difficult expressions to convey the meaning to Korean learners in English.