Everton suffered another blow in their troubled start to the season as they were knocked out of the Carabao Cup on penalties by fellow Premier League strugglers Southampton following a 1-1 draw at Goodison Park.

Sean Dyche’s Toffees went into the third-round tie looking for another boost from the cup, with two more defeats since their 3-0 round two win over Doncaster leaving them with no points from their opening four league games of the campaign and bottom of the table.

They went in front via Abdoulaye Doucoure’s 20th-minute header, but Southampton – also yet to get off the mark this season in the top flight – levelled through Taylor Harwood-Bellis just past the half-hour mark.

With Everton’s Jesper Lindstrom having twice been unable to convert good opportunities, seeing shots saved by Alex McCarthy either side of the equaliser, the tie required spot-kicks for a winner.

It was Russell Martin’s Saints who then emerged triumphant, winning 6-5 after McCarthy pushed substitute Ashley Young’s attempt against the post.

Both sides were much-changed with Everton – who had led 2-0 only to be beaten 3-2 in each of their last two outings, against Bournemouth and Aston Villa – having eight adjustments to their starting line-up, and Southampton’s showing 10.

Everton threatened early on with Beto’s drive being turned behind by McCarthy at his near post, and soon after Dwight McNeil – who had been started in an unfamiliar left-back role – headed over.

The hosts then took the lead when Jake O’Brien kept McNeil’s corner in play and Michael Keane’s header teed up Doucoure to flick in from close range.

Lindstrom subsequently failed to make the most of a great chance to double the advantage, seeing McCarthy save his shot after being played in Doucoure – and six minutes later the score was level as Harwood-Bellis connected with Charlie Taylor’s free-kick to send a header bouncing past Joao Virginia.

After efforts off-target from Keane and, at the other end, Maxwel Cornet prior to the break, Lindstrom found himself through one-on-one with McCarthy once more early in the second half but again could not capitalise as the goalkeeper made another save.

Virginia then made a save to deny Ryan Fraser, before a double substitution by Dyche saw 17-year-old midfielder Harrison Armstrong replaced by Jack Harrison and Beto come off for Young, which was followed by a few boos from Everton fans in the crowd.

Southampton substitutes Ben Brereton Diaz and Tyler Dibling made unsuccessful attempts at a late winner, as did McNeil, Tim Iroegbunam, another to have come on for Everton, and Young as the contest headed towards penalties.

The shootout that followed saw both teams register five successful efforts and James Bree then score Southampton’s sixth, before McCarthy thwarted Young to send the visitors through.