Three late goals consigned the Toffees to a heavy defeat at the hands of the Serie A side, who currently sit 12th in the Italian top flight.
Everton are 16th in the Premier League and their poor form on the back of a significant summer of transfer spending cost manager Ronald Koeman his job.
But their struggles have carried over to the Europa League, too, and under the guidance of caretaker boss David Unsworth they hit their lowest point yet on Thursday night.
Bryan Cristante's double gave Atalanta a two-goal lead before Sandro Ramirez replied with less than 20 minutes to go.
But then Everton fell apart, conceding three times after the 86th minute to end up 5-1 losers.
And Everton have now become only the second English club to pick up just one point from their opening five group games in either the Europa League or Champions League.
The last - and only other - team to struggle to the same extent was Blackburn Rovers back in 1995-96.
Everton's single point came from a 2-2 draw with Apollon Limassol at Goodison Park.
They were beaten 3-0 by both Atalanta and Lyon away from home and also lost 2-1 to the French side in front of their own fans before their latest embarrassment.
They will travel to Cyprus to face Apollon on December 7 but are already eliminated from the competition.
Everton have already lost more games at Goodison this season (five) than they did in the entirety of 2016-17 (four) and are without a clean sheet in 12 games.