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Ander Herrera was sent off for two fouls on Hazard, while Marcos Rojo later appeared to stamp on the Belgian.
N'Golo Kante's 51st-minute winner secured Chelsea a semi-final meeting with Tottenham at Wembley in April.
"In 20, 25 minutes for Hazard, it was impossible for him to play football," said Conte.
"I see only that he got a lot of kicks. I don't think that I'm crazy and I see only him in this situation.
"He started receiving kicks and finished receiving kicks. No one person can say this did not happen."
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Conte was involved in a touchline confrontation with opposite number Jose Mourinho shortly after Herrera's dismissal which ended with the pair being separated by fourth official Mike Jones.
The Italian said he had not seen the incident in which Rojo appeared to tread on a falling Hazard late in the game.
The Argentina defender must wait to see if the Football Association takes action after referee Michael Oliver files his report on the match.
Conte said: "This tactic, to play by going to kick the opponent, does not exist. It's not football for me. I don't think this can be a tactic.
"I think sometimes when you play against players with great talent you try and intimidate these players. I think the referee must protect this type of player."
Conte said Hazard had shown "great character" in a "very difficult and dangerous" situation.
The Italian added: "We go to play football and my players want to play football."
Monday's victory kept Chelsea, who are 10 points clear at the top of the Premier League, on course for a domestic Double.
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Chelsea boss Antonio Conte accused Manchester United of targeting Eden Hazard during his side's 1-0 FA Cup quarter-final win at Stamford Bridge.