Marco Asensio struck both goals for the 2-0 victory.
Emery said afterwards: "We have to be confident but always respecting the opponent and we were trying to dominate.
"The most important was try to be passionate, don't concede transitions of their attacking moment and we did it. Then progressing we had chances. We weren't clinical but the second half after we scored the first goal I think we were thinking OK, our work was going well."
On impact of Asensio and Marcus Rashford, he continued: "It's important for the team, it's important as well for the players individually to get their individual target as well and two goals. He's adapting fantastic, as well Rashford. We will need them for the next matches and the challenges we have.
"We are thinking for the next match. We are in a quarter-final, we are happy. We know the difficulties we are going to face but enjoy each moment and today, here with our supporters, we are here performing at home very well and the cup is very important for the club, for the supporters, for ourselves but as well it is a way for a trophy."