"We are very disappointed that the appeal was lost at this point," Ms Bishop told Network Nine on Wednesday.
"But I understand that the lawyers are considering a further legal avenue and they have about 14 days in which to do so."
Ms Bishop said the government would continue to appeal to President Joko's sense of generosity and forgiveness.
She said she hoped he would consider the clemency pleas and agree to a stay of execution.
"We can only hope that they will see the value of these men's lives, both men have been rehabilitated in the most remarkable way," Ms Bishop said.
Barrister for Chan and Sukumaran, Julian McMahon, has also called the court's decision disappointing, but said he still wants the merits of the mens' case for clemency heard in a court.
President Joko said yesterday that no intervention would stop the executions of Chan, Sukumaran or other foreigners on death row.
Ms Bishop recalled her last meeting with Sukumaran's mother.
"She hugged me so tightly that I could hardly breathe and just begged me to do all I could to save the life of her son, whose own life had been rehabilitated in such an extraordinary way," she said.
- AAP