Palermo sit bottom of Serie A after registering a club record seventh consecutive defeat.
Palermo sit bottom of Serie A after registering a club record seventh consecutive defeat, a 1-0 reverse at home to Lazio, at the weekend.
Coach Roberto De Zerbi has managed to avoid the wrath of the club's trigger-happy owner Maurizio Zamparini, although that was before the Sicilians' latest setback.
Palermo were held to a scoreless draw at the end of extra-time of their fourth round tie at their Barbera stadium, and capitulated to Serie B side La Spezia on penalty kicks.
La Spezia thereby secured a plum tie in the next round with high-flying Napoli at the San Paolo.
Empoli, who sit mid-table in Serie A, were ousted on Tuesday after Alejandro Rodriguez hit an extra-time winner for Serie B outfit Cesena.
On Tuesday Torino booked a last 16, San Siro date with AC Milan, given a bye, with a 4-0 win over Pisa while Chievo will meet Fiorentina away after ousting Novara 3-0.
Cup holders Juventus, plus Roma, Napoli, Inter Milan, Sassuolo and Lazio are not in action until January 11 and 18, when the last 16 ties are held.