Ange Postecoglou mused recently about hope and the inherent futility of it in terms of the way things have gone for Tottenham this season. Every time the manager had seen “light at the end of the tunnel”, he said, it had “usually been an oncoming train”.

He was talking about the club’s injury situation, the crisis that never seemingly ends, and yet the line about the train was an appropriate way to describe Liverpool, who did not so much roll into the Carabao Cup final, their first such showpiece under Arne Slot, as steamroll their way there. They refused to countenance any other outcome. They utterly flattened Spurs.

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Who can stop Liverpool this season? It is the question on everybody’s lips as they look down from the summit of the Premier League and eye glory in the Champions League and FA Cup, too. Nobody believed Spurs would do so here, probably not the diehards who made the trip north and possibly not even the players themselves – certainly not once the reality of what they were facing dawned on them.

It was over, really, when Mohamed Salah scored from the penalty spot early in the second half to give them the aggregate lead – his 26th goal of the season. At that point, Spurs were just about still in it but by now absolutely nobody believed they were. The evidence had been mapped out in graphic detail across the Anfield turf where Liverpool were quicker, sharper, hungrier. Simply remorseless.

Spurs could point to a single flicker in front of goal, the moment on 78 minutes when Son Heung-min pulled off a step-over and blasted against the bar from a tight angle. They had just five shots in total; the rest were eminently forgettable. None was on target.

By then it was 3-0, Dominik Szoboszlai having added further to Cody Gakpo’s first-half opener, and there would still be time for the imperious Virgil van Dijk to add the fourth. It will be up to Newcastle to deny Liverpool in the final. Slot’s team will start as the heavy favourites.

There were the inevitable “Sacked in the morning” chants for Postecoglou from the Liverpool supporters; they have tracked him for weeks and, well, he is still here.

Next up for Postecoglou is Sunday’s FA Cup tie at Aston Villa. What had to hurt him was how little of the adventure and personality he demands were on show. Spurs went with a whimper. And, of course, another injury, Richarlison forced off at the end of the first half to join the 10 players who did not make the trip because of various problems.

It was easy to feel that Liverpool wanted to right a couple of recent wrongs against Spurs from matches in London. There was the Luis Díaz disallowed goal farrago but more pertinently, perhaps, the first leg of this tie, when the midfielder Lucas Bergvall ought to have been sent off rather than allowed to stay on to score the only goal. They did not allow Spurs to play and how they came to do so themselves.

Liverpool turned up the heat as the first half wore on. They dominated possession and their press became an increasing problem for Tottenham. Slot’s team camped in opposition territory and the breakthrough had been advertised, Szoboszlai seeing a goal ruled out for offside from a Salah pass.

When the opener came, it followed a loose Yves Bissouma pass but the error did not happen in a vacuum. This is what Slot’s Liverpool do to you. The ball was worked wide to Salah and when he crossed with the outside of his boot and Darwin Núñez brought a dose of chaos in the centre, it ran for Gakpo. His feet were planted but he was able to summon the power. Should Antonin Kinsky have done more to keep out the shot? Possibly. The goalkeeper was erratic.

Kinsky just about tipped a Salah volley on to the top of the bar in the 44th minute and that was when Richarlison was down at the other end with a calf problem, Liverpool playing on. Richarlison had clashed at the outset with Van Dijk, accusing him of throwing an elbow in his direction. It is fair to say that sympathy from the Kop was in short supply for the former Everton player. Postecoglou introduced Mathys Tel, his new outfield signing, having started his other one, the centre-half Kevin Danso. For both, it was a grisly welcome to the club.

Related: Liverpool make winning look easy as Slot’s machine rolls on to Wembley | Andy Hunter

Kinsky was in the spotlight at the start of the second half. Liverpool brought still more intensity and the goalkeeper did well to repel a Szoboszlai header from a corner. And yet moments later, when Salah played a teasing ball into the area for Núñez, it was possible to foresee the disaster. Núñez was always going to be too quick, Kinsky was never going to pull out of the attempt to claim the ball. All he touched was Núñez. Salah picked out a top corner from the spot.

Liverpool were in no mood to preserve what they had. Gakpo and Ryan Gravenberch both hit the woodwork before Conor Bradley played in Szoboszlai with a lovely first-time pass. The finish was never in doubt. Nor was that from Van Dijk when he rose to meet a corner. Liverpool march on.