I've gone and lost my hat.

Literal

Hat [object-を] lose-[completion-regret-てしまった]

~てしまう (often contracted to ~ちゃう in speech) marks a completed action with an overlay of finality, often regret or unintendedness. Here: 'I lost my hat, and now it's done, and I'm not happy about it.' Subject omitted; the regret tone implies first person.