The Toffees had already been eliminated before the game but caretaker manager David Unsworth selected a strong side featuring Wayne Rooney, Kevin Mirallas and Ashley Williams.
The Italian visitors went ahead after 12 minutes, midfielder Bryan Cristante converting from close range after Ashley Williams’ weak clearance.
With just 17,431 people watching, Everton goalkeeper Joel Robles saved Alejandro Gomez’s penalty and follow-up early in the second half but Atalanta doubled their lead through Cristante’s second.
Sandro Ramirez scored his first goal for the Toffees to cut the deficit but substitute Robin Gosens’ well-struck dipping volley beat Robles before Danish striker Andreas Cornelius’ brace made it worse as Atalanta sealed qualification to the knockout stage.
When Cristante struck the opener, it was the 16th time Everton had conceded first in their past 18 games.
No wonder the small crowd present barely groaned. With summer signing Michael Keane again struggling throughout and Williams slow and clumsy, only second-choice goalkeeper Robles’ heroics prevented an even more humiliating scoreline.
He saved Gomez’s penalty after Williams’ wild challenge on Cristante and acrobatically kept out Martin de Roon’s goal-bound header.
Ramirez’s goal prompted an improved spell from Everton, with 19-year-old midfielder Beni Baningime leading the attempted revival.
But three Atalanta goals from the 86th minute completed a miserable night for the hosts as the Italians secured their first away victory of the season.
