Unfortunately I have to work.
'Purtroppo' — pur-TROP-po. Stress on the second syllable. Clear double 'p'.
Use when work conflicts with social plans. Adding 'purtroppo' (unfortunately) signals that you'd rather be socialising and softens the refusal.
'Devo lavorare' is one of the simplest and most honest cancellations. The addition of 'purtroppo' at the start transforms it from a flat statement into an empathetic apology. It's extremely common and universally understood.
Ho un turno di lavoro.
I have a work shift.
Common for people who work in services, retail, or hospitality
Devo fare gli straordinari.
I have to do overtime.
'Straordinari' (overtime) signals you had no choice — generates sympathy
Mi hanno chiamato a lavorare all'ultimo momento.
They called me in to work at the last moment.
Emphasises the lack of notice — makes the cancellation understandable
In Italy, missing a birthday is taken seriously. The custom of bringing a gift or taking the person out for a separate celebration is common when you miss the main event.