Fulham thrashed Juve 4-1 last night to win the tie 5-4 on aggregate on a famous night for the Londoners.
The defeat came after Sunday's collapse against Siena, which saw Juve pegged back to 3-3 after taking a three goal lead.
Zaccheroni said: "On Sunday we might've considered the game to be over at 3-0, but on an English pitch you should not let the tension drop to that degree."
Fabio Cannavaro was harshly sent off after 27 minutes, but Juve capitulated at Craven Cottage.
"There is no doubt that the defensive element of our team needs to be improved. It's a shame, as we could've gone through and had started well.
"We scored and were positioned comfortably, but the red card fired up Fulham and we struggled under pressure when they put bodies in the box.
"Overall they were sharper and had the great credit of playing a dynamic game."