Doubles from Bryan Cristante and substitute Andreas Cornelius launched Atalanta into the knockout stages with a 5-1 win as Everton turned in another appalling Europa League performance.
Former AC Milan youngster Cristante slotted in an early opener and made the points safe when he headed home after the hour
Captain Alejandro Gomez also missed a penalty for Gian Piero Gasperini's side, who are level on 11 points with Lyon. Group E's dominant teams will play to settle top spot in Bergamo on December 7.
Everton's involvement in the competition seemingly cannot end soon enough, with Sandro Ramirez's fine first goal for the club in the 71st minute coming as scant consolation for a sparse Goodison Park crowd.
Along with beleaguered caretaker boss David Unsworth they endured a late salvo from their Serie A opponents that began in the 86th minute when Robin Gosens brilliantly clattered in from long-range via the post.
One-time Cardiff City misfit Cornelius then twice capitalised on defending pitched some way south of shambolic, leaving Unsworth's long-term job prospects in tatters.
GOOOOOOLLLLLLLLL!!! ANDREAAAASSSS CORNELIUUUUSSSSNovember 23, 2017
A much-changed Everton side captained by Wayne Rooney started on the front foot before being cut apart with galling ease in the 12th minute.
Timothy Castagne got to the byline and, when Ashley Williams failed to clear his low cross, Cristante was left with a simple finish.
Kevin Mirallas benefited from some similarly generous Atalanta defending as the half hour approached but the angle was against him as he shot too close to goalkeeper Etrit Berisha.
The same could not be said for Sandro, who hacked wildly over on the follow-up.
Andrea Masiello made a magnificent headed block on the goalline in the 38th minute to deny Everton youngster Tom Davies an equaliser but the centre-back was limping heavily by first-half stoppage time – his condition compromising a clearance than almost allowed Mirallas to level matters.
Williams sparked an on-field melee in Everton's last Europa League home game against Lyon and another inauspicious outing for the Wales defender took a further wrong turn early in the second period.
Cristante stole clear of Williams, who responded with a desperate lunge that left referee Jakob Kehlet with little option other than to point to the spot.
But Joel Robles came to Everton's aid, springing to his right to keep out a poor penalty from Gomez, who failed to convert the rebound.
Williams kept his goalkeeper busy by glancing a left-wing corner towards his own goal moments later. Joel saved brilliantly once more and Jonjoe Kenny denied Cristante on the line.
Everton's other centre-back Michael Keane was not having a much more enjoyable evening and crumpled to the floor when confronted shoulder-to-shoulder by Hans Hateboer, although the Atalanta wing-back's resulting shot was deflected behind.
The visitors' earlier corner routine paid dividends in the 64th minute when Gomez again threatened the near post from the left and Cristante glanced his seventh of the season into the net.
Atalanta's boisterous travelling support proceeded to shake the Bullens Road stand with prolonged celebrations.
Their din was only briefly punctuated by Sandro arrowing a brilliant finish across Berisha into the bottom corner.
It's 1-2 as nets his first Everton goal! November 23, 2017
That Everton briefly threatened to complete a comeback felt like a trick of the mind as Cornelius made merry in the closing minutes, cutting in to finish sharply before punishing more dismal set-piece defending after fellow sub Gosens had spectacularly sapped any remaining resistance.
