The Toffees had no chance of qualifying prior to kickoff, but failed to restore any pride as they crumbled to a fourth defeat of their European campaign.
Atalanta took the lead on 12 minutes when Cristante finished sharply in a congested box following good work down the right from Timothy Castagne.
Everton were second best for much of the first half but had a couple of chances to equalise as Sandro blazed over from 15 yards, after Kevin Mirallas's shot had been parried.
After Ashley Williams was harshly adjudged to have brought down Cristante, Robles dived the right way to deny Gomez, and then reacted quickly to block the follow-up.
Everton's stand-in stopper showed lightning reflexes again moments later when he pushed away a corner that Williams had inadvertently flicked goalwards, and Jonjoe Kenny hooked Cristante's rebound off the line.
However, there was nothing that Robles could do to keep out Cristante's glancing header from a corner on 64 minutes.
Summer signing Sandro pulled one back with a smart finish across Etrit Berisha seven minutes later, finally opening his Everton account after joining from Malaga.
Rather than inspire Everton, that goal only prompted Atalanta to up their game and the hosts completely capitulated to concede three goals in the final seven minutes.
Gosens sealed the result with a well-taken volley from 20 yards out, opening up his body and beating Robles via the post, before Cornelius took advantage of poor positional play from 18-year-old debutant Morgan Feeney to shoot beneath the goalkeeper for Atalanta's fourth, 68 seconds later.
The one-time Cardiff City striker headed home a fifth in stoppage time as the Serie A outfit booked their place in the knockout stages in style, setting up a winner-takes-all clash with Lyon to see who tops Group E.