This will not rank alongside Liverpool’s most memorable wins of the season. Some of their victories have been devastating displays of attacking football, the sort that make you glad to be a fan. This 3-0 victory against a desperate Stoke City side was not much more than efficient, earned by goals from Sadio Mané and a brace from the substitute Mohamed Salah, but it might end up being among their most satisfying three points.

“It was well deserved, but it was hard work,” said Jürgen Klopp after the game, which might be a little charitable to their opponents, who hardly presented the most fearsome and doughty foes. But it will nonetheless be encouraging for Liverpool that they looked pretty comfortable throughout against a team that set out to frustrate them.

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It could have been different had the referee Martin Atkinson sent off Simon Mignolet in the first half, though. Mignolet rushed out of his goal and hacked down Mame Biram Diouf as the forward tried to round the keeper just outside the area but, as the whole stadium prepared themselves for the sight of a red card, only a yellow emerged.

The rules around sendings-off in those circumstances were relaxed last year, meaning not all such fouls should be automatically considered as red cards. But even though Diouf’s run was angled slightly away from goal and there were defenders roughly in the same postcode, had Mignolet’s boot not intervened he would have had an open goal.

Predictably enough, Klopp had few complaints, but Mark Hughes did. “That’s the key moment in the game,” the Stoke manager said. “I just don’t understand why the officials didn’t see it for what it was. At that point it would’ve been 1-1 and game on. Usually in those situations the home team gets the benefit of the doubt, but we didn’t get that many times this evening.”

Hughes’s complaints might have carried a little more weight if his team had not been so poor, and he should probably have been more irked about their defending than the officials, but Stoke undoubtedly had the rough end of things.

Liverpool’s opening goal was not without controversy, either. The Stoke fans were already unhappy that Alberto Moreno had not been penalised for a challenge on Xherdan Shaqiri, but their ire was raised further when the referee’s assistant ruled that Joe Gomez had kept the ball in on the right byline. Replays suggested at least 9/10ths of the ball had crossed the line, so they may have had a point, but they should be more angry with the way their defence stood still when Solanke neatly laid off the cross to Mané, who delicately lifted it over Lee Grant and into the net. “The one thing you want is for the referee to get the key decisions right, and in my opinion he didn’t,” Hughes said.

Ultimately any refereeing controversy was rendered moot by Stoke’s profligacy and Liverpool’s ruthlessness. Joe Allen missed two fine chances in the second half, one perhaps unluckily deflected wide but the second hoofed way over the bar from around 10 yards out.

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Aside from those chances Liverpool were broadly in control, not necessarily because of their own brilliance (afterwards Klopp said they should have done more with the ball and been tighter at the back), but more due to Stoke’s inadequacies.

With 13 minutes remaining, Liverpool scored again. Mané made Ryan Shawcross look foolish on the right side of the area, zipping around him like a speedboat circling an oil tanker, before clipping a cross to the substitute Salah, who set himself perfectly and hammered an unstoppable volley into the roof of the net.

It was 3-0 a few minutes later. More deeply questionable defending saw Erik Pieters woefully misjudge a header back to Grant, then Salah leapt on the ball and tucked it home with the confidence of a man in the form of his life. Which, as it happens, he is.

All that was left to do was for Hughes to bring on Charlie Adam, as if to remind Liverpool that their team have not always been about lightning fast, dynamic young colts. The away fans spent the remainder of the game merrily singing Christmas songs and suggesting that relegation is on the cards for Stoke. On this evidence, they might be right.