Cristiano Ronaldo's double was overshadowed by Costa's shocking antics at Allianz Stadium, as the former Bayern Munich man was dismissed in the closing stages for spitting at Federico Di Francesco, having already elbowed and headbutted his opponent.
Costa looks set for a minimum three-match suspension and Allegri, who believes that the Brazilian fell for provocation, revealed that a club fine will also be issued.
"It's only right that he is fined, and he certainly will be," Allegri told reporters.
"I was surprised by his reaction. We have suffered a goal, a red card and a suspension which will be long."
Juve's 2-1 victory at the Allianz Stadium ensured that the club maintained their 100% start to the new Serie A campaign, as they bid for their 8th successive Scudetto.
However, it is highly likely that Allegri will have to prepare for life without Costa for a number of weeks in the wake of his ill-discipline, which could see the team lose some of its attacking verve.
The Brazilian was a fixture in the starting XI last season as the Old Lady stormed to a 4th consecutive domestic double and impressed for his country at the World Cup in Russia this summer.
His pace and dribbling ability brings an extra dimension to the Juventus team, but in his absence, they do still have an able-bodied natural replacement in Juan Cuadrado.
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.