The reigning Serie A champions had been hoping to see the Italy international winger remain in Turin, but concede that they cannot offer him the opportunities he craves.
Taking that into account, they are prepared to discuss a transfer with Sunderland.
The Black Cats have been busy bolstering their ranks this summer, with seven deals already tied up, and Giaccherini would represent another shrewd piece of business for Paolo Di Canio.
Conte wishes the 28-year-old well and accepts that sales must be sanctioned if his own side are to strengthen during the current window.
He said: "Giaccherini was valued, they offered him an important contract.
"I'm happy for him but unhappy for me.
"I'm not happy with the sale of Giaccherini but in times of crisis when you buy you must also make sacrifices."