Liverpool are having to stomach “a very bad cocktail” in the Premier League of wasted chances and cheap goals conceded, according to Arne Slot. To extend the mixologist’s analogy, his team are enjoying life with a few margaritas in the Champions League.

Slot’s side cruised into the last 16 for the second successive season with a demolition of Qarabag at Anfield. Mohamed Salah was among the goalscorers for the first time since accusing Liverpool of throwing him under the bus, while Alexis Mac Allister, Florian Wirtz, the potent Hugo Ekitiké and substitute Federico Chiesa were also on the scoresheet.

The biggest victory of his Liverpool reign plus a clean sheet were the perfect tonic for Slot following defeat at Bournemouth. Avoiding next month’s two-legged playoff is an added bonus given his mounting injury problems. Six wins out of eight in the Champions League group, including against both Madrid clubs and Inter, serve as a reminder of the pedigree that Liverpool possess but have failed to show consistently in their troubled title defence.

“We’re happy to be going straight into the last 16, especially as only two years ago we were playing in the Europa League and went out in the quarter-finals to Atalanta,” said Slot, whose team will play either Juventus, Atlético Madrid, Galatasaray or Club Brugge in the last 16. “Now we are two seasons running in the top eight of the Champions League and we are hungry for more this season.”

Slot’s night did not get off to the best start. Already shorn of defensive options and needing Ryan Gravenberch to deputise for Ibrahima Konaté in central defence, Liverpool lost Jeremie Frimpong to injury in the second minute. The full-back pulled up while pursuing a Qarabag clearance down his right flank. Credit to the visiting captain, Abdellah Zoubir, for putting the ball out of play immediately for the full-back to receive treatment. Frimpong has previously sustained two hamstring injuries during his debut season at Anfield and was distraught when limping off. Slot could only confirm this was a muscle injury.

The thought went to Slot’s pre-match press conference, when he defended withdrawing Frimpong against Bournemouth on the basis the Netherlands international was tired and his workload needed managing carefully. “If people knew the struggles we and I are facing, they would be more understanding of the decisions I make,” the head coach had said.

Frimpong’s exit and Wataru Endo’s arrival left Liverpool with a back four comprising two defenders and two midfielders. Virgil van Dijk, Andy Robertson and Milos Kerkez were the only fit, recognised defenders available to Slot although he is hopeful Konaté will return from compassionate leave against Newcastle on Saturday. Joe Gomez could also be back from a hip problem.

Liverpool ensured the disruption had no immediate impact with two goals in quick succession against willing but limited opponents who, thanks to results elsewhere, qualified for the playoffs. Slot’s team took the lead from a set piece, much to his delight. Dominik Szoboszlai’s corner flicked off the defender Kevin Medina and was met at the back post by Van Dijk. His header bounced up for Mac Allister to nod over the line before Mateusz Kochalski could claw clear.

It was soon two when Ekitiké held up Robertson’s ball and spun away from two Qarabag players before squaring inside to Wirtz. A chasm opened up in the middle of the visitors’ defence, giving the Germany international time and space to pick his spot in the bottom corner.

There was no let-up for Qarabag after the interval. In a role reversal of their free-kick routine at Bournemouth, Szoboszlai back-heeled the ball for Salah to sweep a similarly emphatic finish into the top corner. It was the Egypt international’s 49th goal in the Champions League, his first in any competition for Liverpool since 1 November and, notably, his first since that interview at Leeds. Salah pointedly marked the moment by facing the Kop and thumping the Liver bird on his chest.

Ekitiké got the goal his performance deserved when beating one Qarabag central defender after the other to a long clearance out of the Liverpool penalty area. Having sprinted away from both Bahlul Mustafazade and Medina, the striker swept a clinical finish past their goalkeeper.

The visitors’ display was by now disintegrating and Mac Allister claimed his second goal of the night when Matheus Silva sliced a Szoboszlai pass into the path of the Argentina midfielder. Mac Allister duly waltzed around Kochalski and tapped into an empty net. Chiesa completed the rout when Van Dijk surged out of defence and found the Italian striker in space inside the area.

“If we improve in both boxes it is going to be very hard for any team to play against us,” Slot said. “But one game is not enough. We have to do it more often.”