Costa was seen spitting in Di Francesco's mouth in injury time at the end of the game, which Juve won 2-1 thanks to a Cristiano Ronaldo double - his first goals for the club since moving from Real Madrid this summer.
It took the former Real Madrid forward almost 320 minutes to score his first league goal for Juventus and he did it with the simplest of tap-ins.
Khouma Babacar headed one back in the 90th minute but the game ended in ugly scenes as Costa became involved in a running feud with Sassoulo midfielder Federico Di Francesco.
He will now look to end Juventus' 22-year wait for Champions League glory, and the five-time Ballon d'Or victor is eager to return to the competition where he has scored a record 120 goals.
"I also apologize to my teammates, who are always with me in attractive and bad moments".
Next up for Allegri's men is a midweek fixture against Valencia at the Mestalla, as they kick off their latest assault on the Champions League, before returning to Serie A duty with a clash against Frosinone on Sunday. "Obviously, I felt I deserved to start the game", said Bale.
But Bale believes Ronaldo's departure has been good for Real Madrid, with the team not worrying about the Portuguese star anymore.
On Wednesday, he will look to score his first goals in the Champions League in a Juventus shirt.
But Chievo, beaten 6-1 by Fiorentina last time out and on minus points after being deducted three points by the Italian football federation for false accounting, battled back in the second half. "We can't do any of that in Madrid", he added ahead of their midweek trip to Champions League holders Real Madrid.
That has helped Los Blancos to an unbeaten start, though they sit two points behind Barcelona after four games.
Torino was furious when it had an early goal incorrectly disallowed during Sunday's 1-1 draw at Udinese.