West Ham's involvement in the Uefa Cup was short-lived as they lost heavily in Palermo to end their participation in this season's competition.
Simplicio's brace ended West Ham's chances of progression
Fabio Simplicio bagged a brace, his first a low shot that skidded past Roy Carroll, his second a cool lob over the keeper from David Di Michele's pass.
Di Michele completed the scoring with a powerful shot from close-range.
The Hammers paid for their profligacy, with Carlos Tevez, Marlon Harewood and Carlton Cole all missing good chances.
It seems to be the story of West Ham's season in recent weeks, with several spurned opportunities costing them dear both in the Premiership and in Europe.
Starting the tie 1-0 down from the first leg, Alan Pardew plumped for an attacking line-up, with the recalled Tevez partnering Cole and Harewood in attack.
Tevez had the first real chance, latching on to a pass and firing a volley across Alberto Fontana, who tipped expertly around the post for a corner.
After 20 minutes, Palermo sliced open West Ham and Carroll had to be at his best to make a fine double save to deny Di Michele and Aimo Diana in quick succession.
Carroll got injured in the collision with Diana, but he quickly recovered after some treatment, and the Hammers seemed to take heart from his bravery.
First, Harewood forced a flying save from Fontana with a spectacular overhead kick, before the keeper saved brilliantly from Cole's shot and then a James Collins header.
Three minutes later, West Ham's hopes lay in tatters.
Marco Bresciano's short free-kick found Simplicio and his low shot skidded through a crowd of players and beyond Carroll's desperate dive.
The visitors now needed two goals just to force extra-time and Cole wasted another chance when he planted a header wide from close-range.
It was the Upton Park club's last chance, as shortly after Simplicio ran through onto a pass and lobbed over the advancing Carroll to put the tie to bed.
It was harsh on the Hammers, but they had only themselves to blame after creating so many chances without taking any.
With the contest over West Ham fell apart and Palermo wasted no time getting a third, catching their opponents on the counter with the influential Di Michele lashing the ball past Carroll.
Teddy Sheringham came off the bench for what will surely be the 40-year-old's last appearance in European competition, but he could not find a goal to sign off with.
West Ham boss Alan Pardew:
"We had great chances and their keeper made fantastic saves. 1-0 down from the first leg, if we'd scored the first everyone knew it was game on.
"There were not four goals between the sides, but we're big enough to stand up for errors and now we have to focus on improving our Premiership position.
"The difference was quality in forward areas, which is down to confidence."
Palermo: Fontana, Cassani, Zaccardo, Barzagli, Pisano, Diana (Dellafiore 89), Corini (Guana 78), Simplicio, Di Michele (Brienza 85), Bresciano, Caracciolo.
Subs Not Used: Agliardi, Tedesco, Parravicini, Capuano.
Booked: Barzagli, Corini, Cassani.
Goals: Simplicio 35, 62, Di Michele 68.
West Ham: Carroll, Spector, Collins, Gabbidon, Konchesky, Reo-Coker, Bowyer, Mascherano (Benayoun 68), Harewood (Sheringham 68), Tevez, Cole (Zamora 60).
Subs Not Used: Green, Etherington, Mullins, Ephraim.
Booked: Cole, Carroll.
Ref: Georgios Kasnaferis (Greece).