Chelsea reach the last 16 3-1 on aggregate.
Sarri said: "I'm happy for my players and the performance. We played 30 minutes very nervous and without confidence.
"We were better in the last 15 minutes of the first half and after the first goal. It's a good step, I think.
"After the first goal I think we went in confidence and moved the ball very fast and very well. Confidence is very important for playing our football."
On the Carabao Cup final, he added: "It's very easy that Manchester City is in our minds. We played two weeks ago and now we can try to solve this problem."
And On whether Callum Hudson-Odoi will feature, Sarri concluded: "We need to see the situation on Saturday, see what we spent on this match and we need to see the recovery.
"Callum played well but also Christensen and Emerson. We have to consider them for the next match, of course."