The Foxes never got going in Denmark and the hosts failed to take advantage to leave their own hopes of reaching the last 16 in doubt.
Kasper Schmeichel ensured the visitors escaped with a point when he produced a fine last-minute save from Andreas Cornelius, while Christian Fuchs cleared Benjamin Verbic’s effort off the line with Leicester yet to concede in the competition.
Porto’s 1-0 win over Club Brugge meant only a win would send the Foxes through but they lacked imagination in a sloppy, if gritty, performance as their 100% record in Europe ended.
Claudio Ranieri’s side still top Group G by three points ahead of Porto and will be expected to qualify for the last 16 when they host rock bottom Brugge in three weeks.
The Foxes never got to grips with the game as the Danish champions dominated. Danny Drinkwater’s shot deflected wide but it was a rare Leicester chance as Federico Santander headed over after 12 minutes and Wes Morgan blocked Verbic’s strike.
As an attacking force Leicester were non-existent but coped well enough with muted pressure from the hosts although Morgan and Robert Huth were uncharacteristically unsettled.
They handled long balls with ease but both slipped up when Copenhagen attempted to attack through the middle, leaving Huth with a booking after he felled Santander.
That they still held a degree of comfort was more to do with the hosts’ one dimensional efforts than any judgement from the Foxes and Santander sliced a volley wide after 29 minutes as Copenhagen continued to press without penetration.
It took 33 minutes for the Foxes to register their first shot on target when Jeff Schlupp’s weak drive deflected straight at Robin Olsen but it summed up Leicester’s attack on the night.
Riyad Mahrez was shackled while Ahmed Musa failed to make an impact and even a tactical switch of moving Mahrez inside behind Jamie Vardy, who has not scored in 12 appearances, failed to spark the visitors.
Peter Ankersen and Daniel Amartey shared pot shots and Drinkwater’s cross fizzed across the face of goal in the second half but it took until the 59th minute for another real chance.
It was the best opening of the game as Santander teed up Ankersen but the defender fired well over from 18 yards.
Leicester improved, with Mahrez and Vardy linking well, as the game began to open up and Verbic wasted another fine opening when he blazed over Youssef Toulouh’s cross before being denied by Fuchs with 20 minutes left.
Ludwig Augustinsson got free on the left and crossed for Verbic but Austria international Fuchs hacked his effort away at the near post.
Olsen, Ankersen, Jorgensen, Johansson, Augustinsson, Verbic (Kusk 83), Kvist Jorgensen, Delaney, Jensen (Toutouh 65), Santander, Cornelius.
Schmeichel, Hernandez, Huth, Morgan, Fuchs, Mahrez, Amartey, Drinkwater, Schlupp (Okazaki 71), Vardy, Musa.
Felix Brych (Germany).