However, just 77 seconds later, Robert Snodgrass equalised for the Tigers before they went on to win 3-1 during a penalty shootout as the visitors missed three of their four efforts from the spot.
Benitez has acknowledged that he was disappointed to miss out on a place in the semi-finals but he hopes that his players can learn from the experience.
The 56-year-old is quoted by BBC Sport as saying: "The way that we played we deserved to score goals in the first half and in extra time. Then when we did score the goal we didn't manage the situation.
"It's something you learn with experience. Maybe we will do a little better the next time we have this many chances."
Championship leaders Newcastle have now lost two games in a row after also suffering defeat against Blackburn Rovers last weekend.