The Toffees were already out of contention in Group E before kick-off but Unsworth as his side thrashed.
The Italian visitors went ahead after 12 minutes, midfielder Bryan Cristante converting from close range after Ashley Williams’ poor clearance.
Everton keeper Joel Robles saved Alejandro Gomez’s penalty in the 48th minute but the relief was short-lived as Atalanta doubled their lead through Cristante’s second.
Sandro Ramirez scored his first Everton goal to give the Merseysiders a glimmer of hope but Robin Gosens’ fine volley beat Robles before two goals from Danish striker Andreas Cornelius added to the pain.
The defeat ramps up the pressure on Everton to make an appointment to replace Ronald Koeman, who was dismissed on October 23.
Watford manager Marco Silva is hot favourite to take the role and yesterday refused to be drawn on speculation linking him with the job.
The Portuguese coach is one of the favourites to take over at Goodison Park although the Hornets are reportedly unwilling to let him leave. Silva has said very little about his future and, ahead of his side’s Premier League game at Newcastle tomorrow, refused to discuss the issue.
“I don’t like to talk about speculation about these things. I’m here to talk about our match, about Newcastle-Watford, nothing more,” said the 40-year-old.
“Sometimes I talk and after it is going the other way (misinterpreted). I don’t give one more word about this situation.”
Asked if it was difficult to be loyal to Watford who have ditched four managers in three years, Silva said it was a question for owner Gino Pozzo to answer. He said: “If you want, our owner Gino Pozzo (can) come here and you make this question for him, OK?”
Robles, Kenny (Feeney 69), Williams, Keane, Martina, Klaassen (Vlasic 62), Baningime, Davies, Mirallas (Calvert-Lewin 79), Rooney, Sandro.
Pickford, Gueye, Besic, Lookman.
Berisha, Toloi, Palomino, Masiello (Caldara 61), Hateboer (Gosens 70), Cristante (Cornelius 82), de Roon, Freuler, Castagne, Petagna, Gomez.
Gollini, Kurtic, Mancini, Ilicic.
Jakob Kehlet (Denmark).