Roy Hodgson described defeat in his first match as Crystal Palace manager as a painful experience and said his principal task is to prevent his players “digging themselves into a grave”. Palace find themselves rooted to the bottom of the Premier League on the back of no wins and no goals in the opening five fixtures of the campaign – a top-flight record – and they now face a daunting set of fixtures.

Steven Davis’s sixth-minute goal condemned Palace to a deserved 1-0 loss to Southampton and ruined Hodgson’s homecoming after the Croydon-born 70-year-old had been appointed Frank de Boer’s successor as manager at the start of last week. The hosts displayed plenty of endeavour but once again lacked quality and assurance in attacking areas. Their last league goal was scored by Patrick van Aanholt in a 4-0 home victory against Hull on 14 May in their penultimate match of the season and their hopes of maintaining their top-flight status, having achieved promotion in 2013, are already beginning to look bleak. They now face successive trips to the Manchester clubs before a visit from Chelsea.

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“Today I thought it was a disappointing performance,” said Hodgson on what was his first taste of management since England’s defeat to Iceland in the last 16 at Euro 2016 nearly 15 months ago. “The anxiety that was there for all to see in the first half in particular, not made easier, of course, by conceding the early goal.

“It is painful today and I fear it is going to be painful in some of the moments going forward, but there’s no way you can talk yourself out of that and there’s no point in making a bold statement that might not be ratified in some way. We’ve got to just get down to working.

“I’m not suggesting the work we do on the training pitch will produce two or three Messis and Ronaldos but we need to improve our strengths, cover up weaknesses and be analytical in our judgment of the players to ensure we get the best 11 players on the field.”

As well as working his players hard at Palace’s Beckenham-based training ground, Hodgson also said he would also have to work on their confidence, with it clear that they have a severe lack of that right now. “The other [part of our work] is going to be the psychological aspect where we’ve got to try very hard to make certain that people don’t dig themselves into a grave,” he said. “The statistics dig us into a grave, but only what we do on the football field can get us out of it or make the situation worse.”

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Despite the result, Hodgson insisted he was very pleased to be back in management, while it was announced before kick-off that Palace had dispensed with Sammy Lee’s services as an assistant to the former Fulham, West Bromwich Albion and Liverpool manager. Given his links to the club and area, it was also not a surprise to hear Hodgson receive applause from the home crowd when he took his place in the dugout. “I was delighted with the reception I got,” he said.

For Mauricio Pellegrino this was a welcome victory following Southampton’s home defeat to Watford seven days ago. “We are happy about the result, also how we achieved the game from the beginning,” said the manager, who introduced Virgil van Dijk as a late substitute for his first appearance of the season, following the Dutchman’s failed attempt to leave the club in the summer. “Palace got a group of players with quality but we controlled the ball.”