The Black Cats have been mentioned in connection with an £8.6m bid for Giaccherini this week, with extra fees due based on appearances.
Conte has conceded that he has reluctantly allowed the Italy international to join Paolo Di Canio's side primarily to fund bids for other transfer targets.
He told reporters at a press conference this afternoon: "Giaccherini was valued, they offered him an important contract. I'm happy for him but unhappy for myself.
"I'm not happy with the sale of Giaccherini but in times of crisis when you buy must also make sacrifices."
The 27-year-old has played 14 times for his country, featuring for Cesare Prandelli's side last month at the Confederations Cup.