"I knew from the final whistle but I just wanted to give it a bit of time to settle down, talk to my people and then make it clear," Cheika said in video footage released by Rugby Australia.
France, 19-10 ahead at half-time, had Sebastien Vahaamahina sent off for an elbow on 49 minutes but they clung to the lead until Ross Moriarty powered over for the vital try late in the game.
Sharma, on 117, combined with Ajinkya Rahane, on 83, to put on an unbeaten 185-run stand after the hosts were wobbling at 39-3 following their decision to bat first in Ranchi.
England outscored their old rivals four tries to one and had 20 points from Owen Farrell's perfect kicking as they set up a last-four clash with New Zealand or Ireland, who play later.