A surprise selection from the Blues saw the Brazilian, often overlooked during the Premier League season, starting ahead of the PFA Player of the Year favourite for the Wembley showdown with Tottenham.
Willian immediately repaid the faith Conte showed in him with the opening goal, a free kick, after five minutes before scoring from the penalty spot before half-time.
Hazard, who came on in the second half and scored, had no objections, telling BBC Sport: "The manager told me yesterday, you have to expect everything in football.
"When you play football you want to play every game, but he made a great choice. He picked Willian and Willian scored two goals, so it's good for us."
He added: "It's always good to win a semi-final against a London team. It will be my first [FA Cup] final in five years with Chelsea."
Nemanja Matic settled the game 10 minutes from time with a stunning long-range strike which beat Hugo Lloris via the angle of crossbar and post, and was quick to credit Tottenham for a valiant showing.
"We are very happy to be in the final," he said. "When you score four goals against any team, you have to win.
"[Tottenham] are a great team, one of the best in the Premier League. It was very hard today; we scored the first goal, they equalised, we score a second and they didn't give up.
"Congratulations to them, they play good football. That's why we are so happy today."