Froome was forced to withdraw from the elite race after his second crash on wet roads during the fifth stage.
Despite the disappointment, Brailsford believes that the 29-year-old can now turn his attention to winning the Vuelta a Espana later this summer.
Brailsford told reporters: "It was all a bit chaotic. It's just unfortunate for Chris. He has worked ever so hard to be in this shape.
"I'm sure he will be back. I'm sure we will see him in the Vuelta and we will go from there."
Froome, who was due to fly home from the race on Wednesday night, will be replaced as Team Sky's leader by his close friend Richie Porte.