Jürgen Klopp will probably not be collecting his P45 in the morning, as the Wolverhampton Wanderers supporters spent the second half unkindly suggesting, but the Liverpool manager is unlikely to be collecting any silverware this season either after crashing out of two cups in four days.

Liverpool have lost three successive home games, their only victory of 2017 came against Plymouth Argyle of League Two, and their January could get worse with the visit of Chelsea on Tuesday. Presumably Klopp had one eye on that match when he picked a weird, weakened team to face a Championship side in the FA Cup.

Wolves’ Paul Lambert proud but Jürgen Klopp admits: ‘We’re not flying’ Read more

While Liverpool had just about enough experience in their squad to survive, much of it was on the bench and, once they discovered Wolves were up for it as early as the first minute, an unfamiliar lineup never really performed cohesively enough as a team to hit back.

Paul Lambert had promised his side would not simply sit back and defend but would try to break their opponents down and they found that easier than expected. Alberto Moreno gave away the first free‑kick as soon as Wolves crossed the halfway line and Richard Stearman found it simplicity itself to turn up behind Joe Gomez and nod in Hélder Costa’s cross at the far post.

It was a poor goal to concede, especially after 55 seconds, though Liverpool cannot expect defensive understanding if they keep switching the team around so much. Klopp made nine changes from the team who lost against Southampton and the home side could easily have gone further behind in the first few minutes.

Nouha Dicko miscontrolled in front of goal with a clear sight of the target, then Costa set off on a run from his own half that took him all the way into the Liverpool penalty area, only to shoot wide when he had just Loris Karius left to beat. It was no great surprise when Wolves went two up before half‑time, for Liverpool were allowing their opponents to play and presenting very little threat of their own.

Play Video 0:40 Liverpool manager Jürgen Klopp takes responsibility for FA Cup exit – video

Once again Moreno and Gomez will be unhappy with their inability to prevent the goal. When Wolves played the ball out from the edge of their own area and Costa set of on another of his surges upfield, Moreno put in one of his trademark sprints to catch him but did not succeed in winning the ball. Costa retained possession, stayed on his feet and calmly slipped Andreas Weimann in behind Gomez, from where eluding Karius and sticking the ball into an empty net was a formality. Costa was so impressive it was no great shock to hear Lambert say afterwards that Wolves were interested in making his loan from Benfica a permanent move.

“The parties are talking but I can’t influence the finances,” the Wolves manager said. “As a footballer you would take him hands down. He’s got incredible speed and great feet, he’s a huge talent.”

Rather embarrassingly Liverpool had not succeeded in testing the reserve goalkeeper Harry Burgoyne in the whole of a first half in which their only threats of any note amounted to a couple of penalty appeals. Ovie Ejaria’s was the more hopeful, Georginio Wijnaldum was possibly unlucky right at the end of the half, but it was hardly the onslaught Anfield must have been expecting.

Klopp’s response was to send on Philippe Coutinho for the second half, then Daniel Sturridge and Emre Can after him, and even then it took Liverpool until the 86th minute to hit back, when Divock Origi rifled in from close range after Wolves had been unable to clear a corner.

That not only set up a tense last few minutes it also brought the stadium to life for the first time, yet despite Origi bringing a save from Burgoyne two minutes from the end, Wolves were able to hang on.

They might even have gone further ahead when the substitute Jon Dadi Bodvarsson took on the Liverpool defence on his own and almost won, but in the end a single goal advantage was enough. Wolves comfortably kept out everything Liverpool could throw at them and possibly ended up surprised by just how little that turned out to be.

“You could see our supporters celebrating at the end, it’s going to carry on late into the night,” Stearman said, summing up the excitement of an old-fashioned FA Cup upset.

Klopp, having put his side under even more pressure going into Tuesday’s meeting with the Premier League leaders, could strike only a note of contrition. “I could look for excuses, but maybe we should use this time to be disappointed or angry at ourselves,” he said. “All I can say is sorry.”