It was one of those nights when the Champions League music played loud and clear but no one danced to the tune. The entertainment on the pitch did nothing to warm the hearts of the supporters on a chilly night in the Danish capital as Leicester were made to wait for the chance to confirm their place in the last 16.

Claudio Ranieri’s side now need one point from their final two matches to guarantee being in the knockout stage and it would be a major surprise if that landmark moment failed to arrive at home against Club Brugge in a little under three weeks’ time.

They never did enough to pick up the win that would have got the job done here, where FC Copenhagen restricted Leicester to few opportunities and were once again left cursing Kasper Schmeichel. Returning to his hometown and playing in a stadium that is two minutes from his house, Schmeichel produced a brilliant 90th-minute save to deny Andreas Cornelius, just as he did in the game at the King Power Stadium last month, when the same player was prevented from scoring in the closing seconds.

It was an impressive piece of goalkeeping from Schmeichel, especially as he had so little do for so much of this disappointing game. He has kept four successive clean sheets in the Champions League and his importance to Leicester is hard to overstate.

Ranieri described Schmeichel as one of the finest goalkeepers in Europe and it is hard to disagree on current form. “Kasper is fantastic,” the Leicester manager said. “I have coached a lot of big champions in goal, Kasper is one of these. He has had two perfect seasons.”

Ranieri declared himself satisfied with the outcome but far from happy with the pitch, which was recently relaid and caused several players to lose their footing in a scrappy encounter.

On other occasions, especially in the first half, Leicester never helped themselves with some calamitous defensive mistakes that could have proved costly on another evening.

Their centre-backs, Wes Morgan and Robert Huth, were lucky to get away with errors – the latter was booked after he hauled down Federico Santander to stop the striker from escaping – and it took a tactical change from Ranieri, who played with three at the back for a period, to put Leicester more at ease as they struggled to adapt to a new system.

There was no fluency or cohesion to Leicester’s play and they created precious little as an attacking force, with their best moment probably the low centre that Danny Drinkwater slid across the six-yard box early in the second half. The ball eluded Jamie Vardy, who endured a frustrating night in search of his first goal in 12 matches for club and country.

Vardy never had a clear sight of goal, the service into him was poor and the way Leicester set up at the start, with Ahmed Musa also deployed through the middle, simply did not work.

Ranieri accepted that was the case and Musa was shifted out wide with Riyad Mahrez taking up a more central position behind Vardy. There was an improvement for a period, especially during the opening 15 minutes of the second half, but this was far from the Leicester that counterattacked with such menace last season.

In fairness to Ranieri and his players, there was no huge pressure on them to chase a victory because of their commanding position at the top of Group G and a point against a team that is now unbeaten in 31 matches at home, stretching back to August last year, should not be dismissed.

“It was a good performance,” Ranieri said. “At the beginning of the match we expected Copenhagen to push a lot but we stopped them very well and after I changed the shape we played better.”

There were three shots on target all match with Jeff Schlupp registering Leicester’s sole effort with a low, deflected drive that rolled harmlessly into the arms of Robin Olsen, the Copenhagen goalkeeper.

Schmeichel did have one other important stop to make when he smothered at the feet of Benjamin Verbic in the second half.

For much of the game the home team looked toothless up front and although Ranieri praised Leicester for defending resolutely, it was tempting to think that a better side than Copenhagen would have given them a much more uncomfortable ride.

There was some wayward finishing from the home team in the second half, when Peter Ankersen and Verbic failed to make the most of the space that opened up invitingly for them. Santander also thrashed wide after Schmeichel kept out Cornelius’s header with one hand.

Leicester, though, march on and everything is now set up for the visit of Brugge, who have lost all four of their group matches.

“It’s not easy,” Ranieri said. “Yes, Brugge are down but they want to do something. For us it’s important to achieve three points and go to Porto very calm and try to be first in the group.”