The Sky Blues were beaten 3-1 at Hill Dickinson Stadium on Friday in a game overshadowed by key VAR decisions.
In a level first half, Coventry demanded a penalty after Everton defender James Tarkowski appeared to pull Caleb Yirenkyi's hair during a challenge.
The event was checked and cleared by VAR Tim Wood, but Hackett believes it was the wrong outcome and the visitors should have been awarded a spot kick.
"There is no doubt in my view that Everton's James Tarkowski pulled Caleb Yirenkyi's hair," Hackett said.
"It is a clear offence that should have resulted in the award of a penalty kick.
"This should have resulted in a penalty kick and the sanction of a yellow card for unsporting behaviour."
Yann Gboho poked Coventry ahead in the second half before Thierno Barry headed in an equaliser, then quickly notched Everton's second in controversial fashion.
Barry bundled in a cross, and despite an accusation that his hand was used in the process, the goal survived a VAR review and was allowed to stand.
And Hackett feels the match officials made a "massive error" in failing to rule it out.
"You cannot score a goal from the hand or arm even if it is accidental," Hackett said.
"The ball was in contact with the arm of the scorer, so (it) should have been disallowed.
"A huge controversial moment in the game."
Coventry boss Frank Lampard cut a frustrated figure after the game and claimed VAR "didn't do its job," something Hackett believes could land him in hot water.
"Lampard's post-match comments making his observations about the standard of officiating in this game will land him in trouble with the authorities."
