The Blues wanted extra-time to get previous their opponents with the successful objective coming by way of the pinnacle of substitute Pedro.
Earlier, Alvaro Morata gave Chelsea the lead on the stroke of half-time after latching onto a neat by way of ball from Willian earlier than clipping the ball into the online.
Nevertheless, Jamie Vardy’s end from shut vary levelled the tie however the runners-up of final 12 months’s competitors would prevail.
The west London membership shook off a midweek Champions League exit by the hands of Barcelona to ebook their place at Wembley and Conte claimed he felt his gamers deserved to beat the Foxes.
The Italian mentioned: “I feel we have to be happy with the character that we confirmed.
“It wasn’t simple to play towards Leicester as a result of I feel they’re a very good workforce with nice gamers and we should pay nice consideration, particularly once we are attacking as a result of they’ve excellent gamers who assault the house and the defensive position.
“We performed with nice focus and nice want.
“I think my players deserved to reach the semi-finals.”
Morata’s strike was his first since Boxing Day, however the out-of-form striker regarded a modified man on this recreation and his boss was very proud of the Spaniard’s efficiency.
Conte added: “It’s vital [for Morata] to attain and for those who rating your confidence begins to go up in any other case you aren’t comfortable.
“I’m very happy with Alvaro’s performance with and without the ball. He worked hard for the team.”
The ties will likely be performed on the weekend commencing April 21/22.