Conte opted to rest the likes of Eden Hazard and Diego Costa for the London showdown at Wembley, making five changes to his side in all as the likes of Nathan Ake, Michy Batshuayi and Willian all started.
Willian went on to score two first-half goals for the Blues before Hazard came off the bench to add his own name to the scoresheet, and Conte was pleased with how his whole squad responded to the changes.
"I am proud for this achievement. 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," he told BBC Sport.
"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.
"I am very happy for my players and for Michy Batshuayi, he played from the start in an important game. I am happy for Nathan Ake, a young player from our academy. I am happy for Willian, two goals today in a difficult season. For me it is a great achievement.
"Today I also showed I trust all of my team. Eden and Diego knew very well my plan because in this situation it is important to be clear to all of the players. Now I hope on Tuesday to get a great performance from Eden and Diego and the other players."
Chelsea will face either Manchester City or Arsenal in the final on May 27.