Louis van Gaal spent more than £150m this summer to rebuild a Manchester United squad with gaping holes in it. £75.7m of the transfer pot was invested on two forwards to launch the club’s galáctico era. A British record £59.7m went to Real Madrid for Ángel di María, and £16m was paid to Monaco for Radamel Falcao’s season-long loan.

Yet the main problem, the vacuum left by the departures of Rio Ferdinand and Nemanja Vidic, was filled by only one central defender, the £16m signing Marcos Rojo, whose June and July were taken up operating at left-back in Argentina’s run to the World Cup final.

The 1-0 derby defeat to Manchester City left United with 13 points from 10 matches, their worse start since the 1986-87 season when Ron Atkinson was in charge and he would be sacked before Alex Ferguson’s appointment.

United have managed two points from their last three games. The last victory was a month ago against Everton. The points tally is half of Chelsea’s. To be 13 behind the leaders in early November is scarcely credible for the 20-times champions. David Moyes had 17 points at the same juncture last year.

Ferdinand and Vidic continued United’s grand tradition of centre-backs. A lineage who include Bill Foulkes, Martin Buchan, Steve Bruce, Gary Pallister and Jaap Stam. By 1 September Van Gaal had Phil Jones, Jonny Evans, Chris Smalling and Rojo as recognised first-team players plus a clutch of hopefuls in Paddy McNair, Tyler Blackett and Tom Thorpe.

With Evans, Smalling and Jones all injury-prone and yet to prove United defenders of the highest class and this trio supported by three youngsters, Van Gaal’s transfer policy had alarm bells ringing.

The summer pursuit of Borussia Dortmund’s Mats Hummels and Thomas Vermaelen of Arsenal proved fruitless. The German decided staying at his club was a better option and Vermaelen plumped for Barcelona.

Before Van Gaal switched to a conventional four-man defence he deployed the three centre-back system introduced in pre-season for the opening four games.

Van Gaal’s ideal trio had been Evans-Hummels-Vermaelen. Yet when the latter two failed to arrive he used Blackett plus Jones, Smalling, Evans and Michael Keane (before he moved to Burnley on loan) in his defensive trident, as United opened up with a dismal run of results that went defeat-draw-defeat-draw.

Van Gaal deserves credit for ripping up the approach and reverting to the four-man defence United’s rich history has been founded on but results have remained disappointing.

Queens Park Rangers were beaten 4-0, before four unanswered goals in 21 second-half minutes at Leicester City allowed a 3-1 lead to become a 5-3 defeat. United beat West Ham United and Everton, each 2-1, ahead of the three winless matches – draws with West Bromwich Albion and Chelsea, plus the defeat to City.

The side who walked out at the Etihad Stadium for Sunday’s 168th derby featured a winger, Antonio Valencia, at right-back because of Rafael da Silva’s injury. Smalling would add to Van Gaal’s defensive problem by being sent off to join Blackett as a second defender who has seen red and is unavailable for the next game because of suspension.

Yet Smalling can operate in Da Silva’s position. So why Van Gaal did not shuffle him across to right-back, instead of choosing Valencia, and ask McNair, Carrick or Darren Fletcher to start alongside Rojo in central defence is a puzzle.

Instead, following Smalling’s 39th-minute dismisaal and Rojo’s later dislocated shoulder, Van Gaal’s rearguard ended as Valencia, Carrick – a central midfielder making a first appearance following injury – and two 19-year-olds in McNair and Luke Shaw.

Carrick later tried to offer a positive take on his auxiliary role. “I thought we dealt with it OK actually, me playing at centre-half,” he said. “It was my first game back in six months, since the end of last season, so it was a bit of test for me to come on at centre-half. I enjoyed it. It was nice to be back and I have certainly missed it, being out for so long. We will see who is fit and who we can patch up for next week.”

Patching up should not be the United way. Now, the club are 10th, four points from Arsenal in a Champions League position. Guiding United back into Europe is this season’s minimum demand.

On Saturday Crystal Palace are the visitors before the following weekend’s trip to Arsenal. Of where the side go from here, Wayne Rooney said: “We’re working on different things which a lot of us haven’t been used to. We’re progressing each week and playing some nice football. We need to turn that into results and I’m sure we can do that if we keep working, keep learning and keep doing what the manager wants from us.”

What Van Gaal should demand from Ed Woodward in the January window is two premium class central defenders.