What a time it is to be a Crystal Palace supporter. Twelve months ago, the south London club was still waiting to win their first major trophy and even the most optimistic fan could never have imagined that they would be contesting the semi-final of a European competition.

Despite a few anxious moments when a motivated Fiorentina team cut the deficit from last week’s 3-0 defeat in the first leg at Selhurst Park to just two goals with half an hour still to play, Oliver Glasner’s side showed their growing maturity at this level to progress to a last four showdown with Shakhtar Donetsk. While Palace made things far more uncomfortable for themselves after Ismaïla Sarr’s early header, even the loss of Adam Wharton and Maxence Lacroix to injuries before half-time could not knock them off their stride against opponents who have twice been beaten finalists in this competition and gave it their best shot.

After leading them to the FA Cup and Community Shield, Glasner now has the opportunity to sign off at Palace with another trophy after the acrimonious fallout from the Austrian’s announcement he would be leaving in January.

“I think 90% of our players have never played European football before and every single game, every single experience, helps us to grow individually and as a team,” he said before revealing that the Palace squad had been granted a night out in Florence to celebrate their success.

“What’s exactly the same is the players’ aspirations to go out tonight,” said Glasner when asked if he sees any similarities between Palace and the Eintracht Frankfurt team he led to Europa League glory in 2022.

“This was the same as what the Frankfurt players asked when they won the quarter-final. I agreed a few years ago that the players can go out, and I agreed tonight that the players can go out. Hopefully the ending of the story will be the same.”

The Palace fans made the most of the Florentine spring sunshine in the buildup to kick-off, with a large number having travelled without tickets just to experience their first taste of an away European quarter-final. John Salako, the former England winger who was part of the Palace team that finished third in the old First Division back in 1991 but were denied a place in Europe, was spotted enjoying himself in the piazza del Duomo during the afternoon.

With one of the stands completely closed as part of a £160m renovation that will increase its capacity to more than 40,000 by 2029, most of the 1,400 supporters lucky enough to have tickets were crammed into the far corner of this magnificent open-air arena. They certainly made their presence felt when the teams emerged, brandishing giant red and blue flags and letting off red flares as part of a special display organised by influential fans group the Holmesdale Fanatics.

Daniel Muñoz should have settled any Palace nerves within the opening two minutes but the Colombian’s effort was way off target. Yet Fiorentina’s hopes of a famous comeback looked forlorn in the 17th minute when Sarr headed home Muñoz’s cross.

The hosts were given a lifeline when Jaydee Canvot was penalised for catching Rolando Mandragora in what looked like a soft decision from the Spanish referee. To compound matters for Palace, Wharton limped off clutching his groin just before Albert Gudmundsson calmly stroked home from the spot. Glasner later confirmed he has a suspected adductor injury – the same issue that forced him to withdraw from England’s most recent squad.

There was another major setback for Palace just before half-time when Lacroix came off worse than Muñoz after they collided and the France defender was unable to continue due to a knee problem. Fiorentina smelled blood. But Dean Henderson was equal to Tottenham loanee Manor Solomon’s fierce drive on the stroke of half-time to maintain the three-goal advantage. Glasner sent out Jørgen Strand Larsen to warm up during half-time and the Norway striker replaced Jean-Philippe Mateta at the start of the second half. David de Gea did well to save a swerving shot from Daichi Kamada but Henderson could do nothing about Cher Ndour’s piledriver from 25 yards as Fiorentina pulled another goal back. Suddenly Palace’s makeshift defence looked shaky every time their opponents attacked.

The outstanding Gudmundsson forced Henderson into another save as Fiorentina piled on the pressure just before the referee turned down appeals for another penalty as tempers became increasingly frayed.

Chadi Riad was showered with liquid from the stands after making far too much of a push in the back from Ndour but Palace were able to slow the game down effectively. When Roberto Piccoli’s header sailed well over Henderson’s crossbar with nine minutes left, the visiting fans felt suitably relaxed to roll out their new song about making it all the way to next month’s final in Leipzig. Given Glasner’s knack of winning silverware, they will take some stopping.