The Blues emerged 4-2 winners in a thrilling match at Wembley to book their place in the final, putting last weekend's loss to Manchester United behind them.
"I am proud for this achievement," Conte said. "It is great for the players for me. This is my first season in England and it is great to fight for the title and reach the final of the FA Cup, a great competition.
"I am pleased for my players and for our fans. Today they were great from the start until the end. Now we have to continue, on Tuesday have another tough game, I hope our fans push us a lot.
"During the season there is a moment as a coach you must take a strong decision. You have to take a risk.
"If you win the plan worked, if you don’t the responsibility is on you. I think today our plan worked very well."