Conte impressed by Morata's return to scoring form
Spain striker Morata broke the deadlock with a well-taken finish in the 42nd minute as last season's beaten finalists prevailed 2-1 in extra time.
It was his first goal of any kind in 2018, marking a successful return to the starting XI having been overlooked for the last three matches.
The 25-year-old went close to a second on a couple of occasions and won praise for his all-round display.
"For Alvaro it was important to score but I am pleased for his performance," Conte told reporters.
"He showed great character and to be strong. I think his goal will be very important for the future."
13 - Alvaro Morata has scored his first goal for Chelsea since December 2017 (v Brighton), ending a run of 13 games in all competitions without one. Required. pic.twitter.com/5zhe098iQ1
— OptaJoe (@OptaJoe) March 18, 2018
Chelsea, who were beaten by Arsenal in the 2017 decider, were favourably drawn with Premier League strugglers Southampton in the semi-finals.
However, Conte rejected the idea of being in an enviable position.
"I think when you arrive at this point in the tournament it is easy to consider it easy, but Manchester City lost to Wigan," he said.
"I think that we must be ready to fight to reach the final and it will be very important for us. Southampton has the same idea.
"Last season it was a pity to lose the final and not celebrate the double. Our target is to do our best. If we can reach the final I want to change the result."