“Having Mo Salah definitely helps,” said Arne Slot after the Premier League’s leading goalscorer notched twice at Bournemouth to stretch Liverpool’s lead in the title race as the Egyptian continued to write his name in the record books.

A 2-0 win at the Vitality left Arsenal with a deficit of nine points to bridge. “If you want to win here, maybe you need a bit of luck as well, because the margins are so small,” said Slot. Andoni Iraola’s team had previously beaten Manchester City, Arsenal and, last week, Nottingham Forest 5-0 but Liverpool forged on where their rivals had slipped.

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“We knew that if we would have had any chance of a result over here we at least had to compete with them in terms of running and fighting and playing the duels,” said Slot. Bournemouth created several chances, hitting the post twice, but with the goalkeeper Alisson also outstanding, the leaders prevailed.

“Alisson, he was so important again today, two or three absolute world-class saves,” said Slot. “If you want to win here against the team that is so competitive, you need a team performance and work rate; that’s what we have.”

Salah scored his first from the penalty spot after Lewis Cook was ruled to have tripped Cody Gakpo, the decision enraging home supporters. Slot said he assumed it was a correct decision because the VAR ruled in his team’s favour. “One of my players is on a clear one-v-one: either he makes a dive or he touches it,” he said. “I wouldn’t call it luck unless I see and he didn’t touch at all.”

“This penalty can go both ways,” Iraola said. “We played a high level but against the top teams we need to punish them. Small things didn’t go for us. We have given ourselves a chance, but it hasn’t been enough.”

Trent Alexander-Arnold limped from the field in the second half and Slot, although noncommittal on the type of injury, all but ruled the defender out of Thursday’s Carabao Cup semi-final second leg with Tottenham: “It’s never a good sign when a player is asking for a substitution.”

Alisson joined the tributes to Salah, who had overtaken Frank Lampard to become the Premier League’s sixth all-time goalscorer on 178. “He is quality, he knows how important he is for the team when he scores. Defending is something he doesn’t like to do, but he does it for the team.”

Virgil van Dijk, at a similar contract impasse to Salah, said: “Let’s make it more, let’s keep going. He has obviously been amazing for the football club over all those years.”

“It feels good scoring goals and the team winning,” said Salah.