At last, the Fulham support had a cup tie. For so long, it felt as though their big night would fall flat. Liverpool had scored early through Luis Díaz and it was not a moment that the Fulham goalkeeper, Bernd Leno, will enjoy watching back.

Fulham needed two goals to take this Carabao Cup semi-final to extra-time and it was Liverpool, fighting to remain alive on four fronts, who boasted the assurance. It said so much that when the Fulham playmaker, Andreas Pereira, misplaced a pass on 66 minutes, there were boos from the crowd.

The fans who had turned up for a rare semi-final for their team – only the eighth in their 145-year history – had wanted to see something, anything, to give them hope. Now it came. There were 76 minutes on the clock when the substitute, Harry Wilson, tricked past Conor Bradley to cross and, after a slight deflection, there was Issa Diop, to guide the ball home with his thigh.

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Cue delirium, which almost got completely out of hand moments later when Wilson strode forward to shoot, the ball so nearly squirming out of the grasp of Caoimhin Kelleher and in. “Stand up if you still believe,” roared the white and black hordes, as they had done here, famously, during their previous semi-final, second-leg – against Hamburg in the 2009-10 Europa League.

That night, their team pulled off a comeback victory for the ages. This time, it would prove beyond them, the noise at full-time coming from the visiting enclosure. Liverpool march on – and nobody could say that they did not deserve to do so. For Fulham, there was heartbreak.

The buzz was palpable, the potential for an I-was-there night clear; at least that was the pre-match hope. Fulham do not play these type of games with any kind of regularity and the stadium announcer had been keen to talk up the scale of it; to remind the home fans of their responsibilities, too.

Jürgen Klopp’s idea was to tweak the engine and keep Liverpool purring. No top-flight manager has rotated more than him this season and the headline item was the selection of Jarell Quansah ahead of Ibrahima Konaté in central defence. Also in at the start were Kelleher, Ryan Gravenberch and Cody Gakpo.

The Fulham supporters had waved their black and white flags when the players emerged for kick-off, the pyrotechnics also going off. ‘Dare to Dream’ read a banner in the Hammersmith End. All of which made Díaz’s early goal such a passion killer.

Fulham had flickered in the early exchanges, especially when João Palhinha arrived on the penalty spot to meet an Andreas Pereira corner. Palhinha was unmarked and he had plenty of time to read the flat delivery. He lifted the volley high and, as Marco Silva put his hands up to his head, the thought occurred that Fulham might live to regret the spurning of such a chance, even if it was hardly a sitter.

Quansah played a big part in the goal that saw Liverpool put the tie in a vice-like grip, shaping a long crossfield diagonal, right to left; the sort of pass that Klopp’s team habitually look for, how they get them up and running.

Díaz went up with Timothy Castagne and he won the duel too easily, collecting the ball on his chest and surging inside. When Tosin Adarabioyo and Palhinha converged, Díaz shot and what happened next was difficult to unpick. Suffice to say that the ball deflected to flummox Bernd Leno at his near post. The goalkeeper beat the ground in frustration. It was a horrible one to concede.

The home crowd were desperate for anything to get behind. There was not too much across the remainder of the first-half. Raúl Jiménez shot low for the far corner and Kelleher made a decent save. There was plenty of howling at the referee, Simon Hooper, but it was not as though he got anything wrong before the interval.

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Liverpool were unflustered in possession in the first half. Where was the hustle from Fulham? The red shirts relished the physical battles and they might have added to their lead. Darwin Núñez threatened, a few nearly-but-not-quite moments. Harvey Elliott looked as though he enjoyed the boos that came his way as an ex-Fulham player; he demanded the ball and tried to make things happen. Leno, meanwhile, was relieved to see an offside flag go up after he punched an Elliott cross into Gakpo and watched the ball fly narrowly wide. It was a very close call.

Silva was in an extremely tricky position at the start of the second half. He had to drive greater inroads into Liverpool territory and that surely meant committing more men forward. Yet that would dice with disaster against Liverpool’s rapier-like counters. Díaz is not the sort of player to leave with green grass in front of him. Nor is Núñez.

Díaz had gone close on the break when Fulham thought they had a lifeline. Adarabioyo reached a Willian cross ahead of Kelleher to head towards the left-hand side of the six-yard box. The angle was tight for Pereira and he crashed his shot against the outside of the post.

It said plenty that Liverpool went straight up to the other end and nearly scored themselves. Núñez played the final pass and Elliott, with only Leno beat, shot too close to the goalkeeper’s legs. Leno would also save brilliantly from a Núñez curler while the Liverpool centre-forward would be inches from finding the far top corner after a smart spin.