It is a measure of Oliver Glasner’s confidence in his own ability that the Austrian has never been afraid to crack a joke. Back in 2019 when he had just guided Wolfsburg to a nine-match unbeaten spell after joining from Lask – where he served simultaneously as the director of sport and head coach – the former defender was asked whether it had been a big step up to the Bundesliga. “For me it was 680 kilometres, a fairly big step,” he responded. “But other than that I don’t feel it’s such a big step up.”

Fast forward nearly five years and after less than three months in charge of Crystal Palace, Glasner has shown the Premier League he deserves to be taken seriously. Monday’s 4-0 thumping of Manchester United meant his side have scored 11 goals in their past three matches at Selhurst Park and taken more points – 13 – from their past five matches than anyone other than Manchester City. No wonder Glasner made light in February at his first press conference of a question about the possibility of following in the footsteps of Frank De Boer by being sacked by Palace after four games. “I could have stayed in Austria and gone skiing,” he said.

Related: ‘We let each other down’: Ten Hag admits Manchester United at new low

Yet for Palace’s chairman, Steve Parish, the summer promises to be a seismic challenge after he was again forced into a mid-season managerial change as results deteriorated rapidly under Roy Hodgson.

Glasner appears to have the right formula for success with an innovative 3-4-2-1 formation that has allowed Eberechi Eze and Michael Olise to flourish in attack after they missed large chunks of the season through injury. But questions remain about whether Palace can retain what the manager who guided Eintracht Frankfurt to Europa League glory in 2021 has described as “an amazing group”.

Eze and Olise have signed new contracts in the past 12 months but are believed to have release clauses – albeit of more than £60m – and the England defender Marc Guéhi has also been heavily linked with a move as he approaches the final two years of his deal. Work is expected to begin on the new main stand in the summer – more than six years after Palace were granted planning permission. Funding a project that could cost more than £150m to increase the capacity to 34,000 may force at least one star to be sold.

Much of the credit for assembling the squad must go to Parish and the sporting director, Dougie Freedman, who is of interest to Newcastle and has been linked with a move to Manchester United’s backroom staff as part of their new setup under Ineos. The former Scotland striker’s eye for talent in the Championship in particular has paid off handsomely for Palace, with Adam Wharton – who joined from Blackburn a few days before his 20th birthday for an initial £18m – outstanding in the revival under Glasner. His performance against United and an under-par Kobbie Mainoo could not help but catch the eye of Gareth Southgate in the stands, although it may be just too late for a European Championship call-up for the midfielder.

Eze, who joined from QPR in 2020 and was the subject of interest from Manchester City last season, may have done enough to earn a place in Southgate’s expanded 26-man England squad after missing the last squad due to injury; he was a regular for most of last season, along with Guéhi. Olise’s international future remains intriguing given that he is eligible for Algeria, England and Nigeria as well as France, for whom he is an Under-21 international. He is expected to play for France at this summer’s Olympics under Thierry Henry.

Several of Palace’s less heralded players have made significant improvements under Glasner. Jean-Philippe Mateta has blossomed into one of the division’s most effective strikers, scoring in six successive home league games – the first time anyone has managed that since Alan Shearer under Kevin Keegan at Newcastle in 1996. Tyrick Mitchell has rediscovered the form that earned him two England caps in 2022 as a flying wing-back, with the new signing Daniel Muñoz performing a similar role on the other flank, while Will Hughes, Chris Richards, Jefferson Lerma, Joel Ward and Nathaniel Clyne have adapted brilliantly to the new system pioneered by Glasner at SV Ried a decade ago after a spell as Ralf Rangnick’s assistant at Red Bull Salzburg.

Guéhi’s return as a substitute against United should give Glasner even more optimism about matching Palace’s record Premier League points tally of 49, achieved in 2018-19 under Hodgson. That would require victories in their final two matches, against Wolves and Aston Villa, which does not look beyond a team clearly buying into Glasner’s philosophy.

“It’s all credit to the character of the players, because they trusted us from the first day,” Glasner said. “They listened, they tried and they worked really hard in training and now they get their reward.” Palace supporters are hoping there is a lot more to come.