Charlie Austin gave the London outfit the lead on two separate occasions, but Benitez's men firstly drew level through Lucas Digne, before Andros Townsend levelled the scores at 2-2 early in the second half.
With the game finishing 2-2 after 90 minutes, the sides went straight to a penalty shootout, and having each scored their first seven spot kicks, Tom Davies's denied effort was decisive, resulting in the Toffees' exit from the competition.
Speaking to evertontv, Benitez said: "I am very pragmatic, I am disappointed – I will be disappointed maybe today and tomorrow but I will start working already on the next game and it is another challenge for us."
Turning his attention to their return to Premier League action, the Spaniard continued, saying: "If we work in the same way we did today and the attitude is similar, we will improve the other things and, little by little, the team will be more consistent, more solid."
The Merseyside outfit welcome basement side Norwich City to Goodison Park on Saturday, having lost their last league game 3-0 to Aston Villa, while the Canaries are without a point from their five top-flight games so far. body check tags ::