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The Championship high-flyers left it late to stun Jose Mourinho's men in the quarter-final earlier this evening.
Chelsea will take on Arsenal in the semi-final, while Bristol must travel to the Etihad first to take on Pep Guardiola's Manchester City.
And Conte was pleased to see the holders of the competition and fellow Premier League heavyweights United knocked out before the last four.
"It’s a great achievement," he said.
"Manchester won the competition last year.
"You must pay attention in every game.
Chelsea player ratings v Bournemouth
Chelsea FC
“It’s a great achievement”
Antonio Conte
"These cups are very good for these types of surprise.
"I knew the final result in the changing room.
"It’s a surprise but in England it’s difficult to face every team."
Chelsea may have given up in their quest to retain the Premier League.
But Conte's men are still fighting on four fronts this season.
And the Italian insists his side will continue to fight.
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"We will fight to the end for every competition," he added.
"To reach the semi-finals is a remarkable achievement for the club.
"We want to try and reach Wembley.
"The other teams want the same."
Chelsea take on Everton this Saturday (12.30pm).