Used to express mild disappointment, embarrassment, etc.
(colloquial) Exclamatory response to a minor disappointment.
Shucks. It's too bad you can't make it to the party.
(colloquial, sarcastic) Response to a minor pleasure.
Shucks, I guess we'll have to take all this pie home with us.
Aw, shucks, ma'am, catching those wild horses was easy.