Ref Rob Shoebridge has paid the price for failing to award Crystal palace a clear goal during Saturday's Championship match between Palace and Bristol City at Ashton Gate.
Palace striker Freddie Sears looked to have given his side the lead after 34 minutes when he drilled a low shot into the corner of the net.
Shoebridge inexplicably awarded a goal-kick with neither himself or Holmes spotting the ball had crossed the line.
Hackett confirmed Shoebridge has been removed from taking charge of the league clash between Plymouth and Cardiff at Home Park on Tuesday. His assistant Chris Knowles has received the same penalty.
Hackett recognises the need for technology to be implemented, but is aware it will not happen unless FIFA and Sepp Blatter alter their stance.
Hackett, general manager of the Professional Game Match Officials Board, told Press Association Sport: "I think the major issue centres around the fact for a number of years PGMOB have been calling for goal-line technology to be introduced.
"In fairness the Premier League worked with Hawkeye to achieve a product that the Premier League wanted to put into an operation as an experiment with the full support of the Football League, Football Association, LMA and PFA.
"All the parties were in favour but, at the international board meeting in Gleneagles a year ago, FIFA and Sepp Blatter decided the experiment could not go ahead.
"All we are looking for is fairness, to the players and the manager and the supporters, and we want a support mechanism to say 'is it a goal or not a goal.'
"The ref carries the can with his colleagues but we've already said we need help in this particular field. Until the international board change their mind, we can't do anything."
Hackett confirmed: "He (Shoebridge) was scheduled to do a game in mid-week. He won't be doing that. The ref has been spoken to.
"It applies to the referee's assistant as well. Ideally you want the assistant looking from one angle and the ref from another.
Therefore between them you want the decision to be right.
"There are two sides to it. You don't want to negatively effect the confidence of the ref but we are also protecting him.
"If you are involved in that type of decision, it is good to have a few days away and reflect and we will examine and talk about it and how we can avoid it going forward."