Sulley Muntari's penalty gave Pompey a shock victory at Old Trafford and a place in the last four of the competition, ending United's chances of repeating the 1999 treble of Premier League, FA Cup and Champions League.
Ferguson was unhappy that his side had been denied a penalty when Cristiano Ronaldo was blocked by Sylvain Distin.
"It's absolutely ridiculous," he said.
"I cannot explain it. Managers get sacked because of things like that and he's going to referee a game next week.
"He (Hackett) is not doing his job properly and he needs to be assessed.
"I'm assessed as a manager, players are assessed, referees should be assessed properly by the right people. That performance today should not be accepted by our game."
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