The Bianconeri surrendered the initiative having fought back from a goal down in Turin, leaving them with two points from their opening two games, with a double header against Real Madrid coming up.
"Now it's an uphill struggle, but we must not get downhearted," Conte told reporters.
"We've got to fight with the dagger between our teeth. If we do well then we will go forward, if we don't then it'll mean the others were better and we tip our hats to them."
Los Blancos top Group B with two wins from two.