Julian Nagelsmann, Hoffenheim’s bright young thing of a coach, proclaimed he was not in awe of Anfield but his team were overawed, overrun and overwhelmed by the attacking prowess of Liverpool. Jürgen Klopp’s side released 15 months of frustration to seize their second shot at the Champions League in emphatic style.

A mesmerising display from Roberto Firmino, Sadio Mané and Mohamed Salah ensured the likes of Barcelona will not be Liverpool’s competitors only in the transfer market this season. They dismantled the European debutants in an early onslaught that yielded two goals for Emre Can and one for Salah before Firmino capped an outstanding contribution with Liverpool’s fourth.

Hoffenheim refused to wilt even with the tie quickly beyond them and defenders running around like “headless chickens”, to quote their honest and overly-ambitious coach. Consolations from Mark Uth and Sandro Wagner diminished Liverpool’s comfort levels but, after missing the chance to rejoin the European elite when losing the Europa League final to Sevilla in May 2016, this time Klopp’s team seized the opportunity to shape their entire season for the better.

For only the second time since they acquired Liverpool in 2010 Fenway Sports Group preside over a club in the Champions League group stages. The extra revenue will be welcomed, naturally, but the price of qualification had no monetary value at Anfield on Wednesday. After an arduous campaign to reach the play-offs and a pre-season overshadowed by Barcelona’s relentless pursuit of Philippe Coutinho, plus their own dead-ends in the transfer market, a return to the European elite marks a significant step forward for Liverpool under Klopp. His emotional reaction after the final whistle was as much a release as a celebration.

Positive pressure, Klopp had called Liverpool’s 2-1 advantage entering the second leg of the play-off, and his team thrived on it. The teams served up another breathless encounter but unlike in Germany the opening exchanges flowed one way. Liverpool’s way. After 21 minutes of attacking excellence they had Hoffenheim beaten and secured the Premier League five places in this season’s Champions League. By the 24th minute Nagelsmann had no alternative but to tear up a game-plan that played to his opponent’s strengths and go for broke, sacrificing the hapless Havard Nordtveit and introducing another striker with Liverpool running riot. Mané, Firmino and Salah were irrepressible and destroyed their opponents at will.

Liverpool were on the front foot from the first whistle. In fairness to Alberto Moreno, roundly criticised for his performance in Germany, he repaid Klopp’s show of faith in keeping the same starting line-up by helping set a relentless tempo. Salah and Mané had both gone close when Firmino, having created the Senegal striker’s first chance with a superb diagonal ball behind Nordtveit, repeated the trick behind the former West Ham United defender. Mané’s run was checked by Kevin Vogt and so he responded with a backheel into the path of the over-lapping Can. The Germany international’s shot was heading across goal before a deflection off a covering defender left goalkeeper Oliver Baumann wrong-footed and beaten.

Firmino was unplayable and helped double the home side’s advantage on the night when, dancing in from the left, he picked out Georginio Wijnaldum with a low cross that the midfielder side-footed against a post. Salah, unmarked and onside, converted the rebound from close range.

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The third arrived within two minutes and will live long in the memory as an outstanding team goal. Firmino, yet again, was at its heart. The Brazil international was involved at the start of the move when he laid off Moreno’s pass into Wijnaldum inside his own half. Wijnaldum’s first time ball released Mané down the left who, spotting Firmino’s remarkable run, delivered another backheel into the path of his overlapping team-mate. Firmino chipped an inch-perfect cross to the back post for Can to volley home from close range. “That’s football!” screamed Klopp on the sidelines. A stunning team goal.

His hopes and defence in tatters, Nagelsmann had to act and introduced Uth for the frequently exposed Nordtveit. In fairness Hoffenheim responded well to the change in shape and it was a sign of their improvement that Klopp had become exasperated before Uth, scorer of his team’s consolation in the first leg, struck again. Serge Gnabry produced an awful finish when played through by Andrej Kramaric, clipping the ball over Simon Mignolet but also yards wide of the far post. It was left to Uth to show his team-mates how to finish. Wagner released his fellow forward clear on the right and Uth beat Mignolet with a precise low shot into the far corner.

Anfield was not in danger of witnessing another remarkable European comeback, however. Liverpool maintained control and the ability to hurt Hoffenheim after the restart. Wijnaldum, released by Salah, fired over from only six yards out and Mané tested Baumann with a blistering shot from the angle before Firmino was presented with the goal he merited.

Jordan Henderson made the fourth by hunting down an under-cooked pass by Kerem Demirbay and beating Vogt in the tackle and racing through on goal but selflessly squaring for Firmino to finish beyond Baumann, before Wagner reduced the deficit with a towering header from Andrej Kramaric’s cross.

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