There was nothing riding on the Europa League game for the already-eliminated Toffees but the visitors found it all too easy as they secured qualification, even discounting a missed penalty from captain Alejandro Gomez, with two goals from Bryan Cristante early in each half.

Sandro Ramirez's first strike for the club he joined in the summer gave the hosts something to fight for late on but goals from substitutes Andreas Cornelius (two) and Robin Gosens in the closing stages typified Everton's haplessness.

Caretaker coach David Unsworth's evaluation of the game's importance was evident in nine changes - retaining only Michael Keane and Jonjoe Kenny from Saturday's draw at Crystal Palace - that saw Davy Klaassen make his first start since being hauled off at half-time against Lyon a month ago and Sandro in the XI for the first time since September 28.

On the basis of their performances, along with the likes of Kevin Mirallas and Cuco Martina, it was easy to understand why they have been marginalised.

The second-lowest Goodison crowd in Everton's European history - the 17,431 beaten only by the 1,200 fewer who watched the European Cup Winners' Cup game against University College Dublin in 1984 - endured a grim night.

Everton lacked purpose, intent, a seemingly coherent plan and their shape could at best be described as fluid, at worst shambolic.

Exactly a month since Ronald Koeman was sacked, Unsworth's record is four defeats, a win and a draw with 15 goals conceded and six scored.

While the interminable search for a replacement drags on, RB Leipzig's sporting director Ralf Rangnick was the latest to be linked, the club's under-23s coach is not making much of a case for an internal appointment.

Everton's last clean sheet came in the Carabao Cup win over Sunderland on September 20 and it took just 12 minutes for Atalanta to extend that wait with a goal which owed as much to the Toffees' apparent disinterest as the visitors' own creativity.

Martina and Klaassen collided and failed to react as Timothy Castagne ran unopposed down the right, skipping past a half-hearted challenge from Keane and crossing for Cristante to shoot into an open net.

On the half-hour Mirallas' extra touch narrowed the angle, goalkeeper Etrit Berisha saved and Sandro blazed over.

That was the start of their best spell with Tom Davies' shot headed off the line by Rafael Toloi and Mirallas drilling straight at the goalkeeper.

Normal service resumed three minutes after the break when Williams, already booked, was lucky to concede only a penalty after bringing down Cristante despite replays suggesting he touched the ball.

Joel Robles saved Gomez's spot-kick and follow up but, after the goalkeeper prevented Williams scoring an own goal and Kenny headed off the line, Cristante out-jumped three markers at the near post to make it 2-0.

Sandro's angled shot pulled one back with 18 minutes to go but Keane being penalised for a foul as his header bounced off the crossbar and onto the line was as close as Everton came to an equaliser.

Gosens and Cornelius put them out of their misery to secure Atalanta's first European away win since 1991.