It was no exaggeration to describe this as the biggest match of Southampton’s season. It was not for Liverpool, who have their designs on the Premier League title but for Claude Puel and his players, the first leg of the EFL Cup semi-final represented a tantalising opportunity.

The top six in the league has come to look like a closed shop, with Southampton among the clubs with their noses pressed up against the window outside and so, the chances are, Puel will not be able to improve on last season – when Southampton finished in sixth place. Unless he were to win a trophy. That would make it different. That would make it one of the greatest seasons of all time for the club. Southampton, remember, have only ever won one major trophy – the FA Cup in 1976.

They are now 90 minutes from only their sixth major final – two of those came in 1900 and 1902 – and they put themselves in the position with a performance of discipline and no little style against a Liverpool team that simply failed to turn up.

Nathan Redmond’s goal was the difference but Southampton were left to rue a clutch of misses that might have put them in complete control. Redmond was twice denied by Loris Karius in the first half – the second chance was a glorious one – while Cédric Soares fluffed a counter-attack in the second half while, towards the end, following another quick break, Redmond watched his deft chip sail over the Liverpool goalkeeper but come down off the underside of the crossbar.

Liverpool offered nothing – apart from Roberto Firmino’s early snap-shot, which forced Fraser Forster to touch over – and the moment when Adam Lallana, the former Saint, screwed a shot so far wide in the 59th minute seemed to sum things up. The home support were entitled to ask what on earth it was from Lallana – or words to that effect.

Southampton had entered the game at a low ebb; a run of three straight league defeats and the FA Cup draw at Norwich City bringing the grumbles about Puel and his style of play back to the surface. Liverpool, by contrast, had lost only twice all season. But after a tepid start, it was Southampton who took charge and, at 1-0, it was set up for them to punch on the counter. They so nearly landed the knock-out blow.

Klopp had brought back the big guns, after the youthful experiment against Plymouth Argyle in the FA Cup. This was as strong a line-up as he could have selected and there was the added bonus of Philippe Coutinho being back as a substitute, after his near seven-week lay-off because of ankle ligament damage. Coutinho came on in the 62nd minute and he showed a few flickers. Klopp talked of that cameo as one of the few positives – together with the defiance of Karius.

It was a night when Daniel Sturridge got no change out of the outstanding Virgil van Dijk – the Liverpool striker struggled sorely – but he was not the only one. Klopp tried to change things in a novel way on 73 minutes when he sent on a note to Sturridge, which detailed a formation switch to 3-5-2. Sturridge passed it to his teammates and, for a moment, confusion seemed to grip. Klopp admitted afterwards that he could not explain the performance of his team.

Redmond’s goal had a spiritual dimension. Jack Dowding, a 20-year-old Southampton supporter, had died suddenly last Saturday and there had been a campaign – driven on social media – to honour him with applause in the 20th minute. It was easy to sense that a higher power was at work because the goal came on 20 minutes. As Redmond and his team-mates celebrated, there was the uplifting sight of thousands of Saints fans remaining upstanding to applaud Dowding.

The goal followed a ball forward from Dusan Tadic and an ugly swipe and a miss by Ragnar Klavan, which saw it break for Jay Rodriguez. He slipped a pass inside for Redmond, who had broken clear and, confronted by Karius, he finished confidently.

Ryan Bertrand had sparked Southampton with a storming run from inside his own half in the 19th minute and, moments later, Soares crossed for Redmond and he was denied by Karius. The goalkeeper could do nothing about the goal while he blocked in dramatic fashion from Redmond just before half-time, after good work by Bertrand and a low cross from Tadic.

Klopp applauded Coutinho after the Brazilian had burst through to win a corner, but from it Southampton broke through Redmond and when he played in Soares on the overlap, Rodriguez was available in the centre for the cross. It was two-on-one at that point but Soares took on the shot and it hit the side-netting. Puel buried his head in his hands.

There would be more frustration for Southampton. On 84 minutes, the substitute, Shane Long, burst away from Lucas Leiva to cross for the all-action Redmond but he was denied by the woodwork. Liverpool live to fight another day.