Everton caretaker manager David Unsworth said “things have to change quickly” at the club after their poor run continued with a 4-1 defeat at Southampton.
Saints striker Charlie Austin scored two second-half headers on his first league start of the season as the Toffees capitulated after half-time.
They have now won only once in seven games under Unsworth.
“It’s killing me,” said the 44-year-old former Everton defender, who urged the board to quickly appoint a permanent manager.
“I take responsibility, but we all have to as well. We’re in a tough place and things have to change quickly.”
Unsworth said the performance at St Mary’s was “not acceptable” and the team needed to “get back to basics”.
He added: “Confidence is as low as it has ever been.
“The club has to decide and the sooner that happens the better. The players need this resolving.
“What I see is a happy squad but I’d rather have an unhappy squad that’s winning. I want what’s best for the club and I hope the players do too.”
Dusan Tadic gave the hosts an early lead but Everton’s record signing Gylfi Sigurdsson levelled just before the break.
After Austin’s double, Steven Davis scored from the edge of the box to wrap up victory for the Saints, who had previously scored only six league goals at home this season.
Mauricio Pellegrino’s men produced a vibrant attacking display that should lift the pressure on the Argentine after his side failed to muster a shot on target in the 3-0 defeat by Liverpool.
With Ryan Bertrand and Cedric Soares offering a constant threat down the flanks, and Austin intent on making his mark, the Saints could have scored more.
Austin hit the post after 11 minutes following tenacious work out wide from Soares, and defender Virgil van Dijk headed wide on 40 minutes following James Ward-Prowse’s corner.
This defeat came just three days after a 5-1 loss to Atalanta in the Europa League, and ex-Everton striker Gary Lineker described the club as “a shambles” as they collapsed at St Mary’s.
The Toffees seem rudderless on and off the pitch, and former defender Unsworth has been unable to add any stability since Ronald Koeman was sacked in October.
Everton have now conceded 28 goals in the Premier League this season – their worst tally after 13 games since 1958-59.
Their only win under Unsworth came on 5 November against Watford, whose manager Marco Silva has been a target for the Toffees.
But, with the Portuguese seemingly now off the agenda, it is difficult to work out if the club had a plan for life after Koeman.
A worrying lack of clarity over their manager search is echoed on the pitch, where capitulation follows capitulation and the players’ body language looks increasingly forlorn.
Something has to give and fast – because they are playing like a side with very real prospects of going down.
Austin, Tadic, Bertrand – men familiar to the Southampton faithful had big games against Everton.
Austin’s double means he has had a hand in eight goals in his past 11 Premier League starts and gives Pellegrino something to think about when it comes to selecting his team for Wednesday’s game at Manchester City.
Tadic, meanwhile, has now been directly involved in 40 league goals for the Saints, and Bertrand provided two assists and impressive energy.
But, while the headlines will go elsewhere, a 22-year-old who had played for just six minutes this season also stood out.
Pierre-Emile Hojbjerg looked bright in pre-season but his progress has since stalled.
Against Everton, he showed eye-catching industry and efficiency – making more passes (96) than any other Saints player.
He was more accurate with his distribution than any of his midfield colleagues and also made more tackles than anyone else on the pitch – not a bad way to put yourself firmly back in your manager’s plans.