Luiz Adriano hat-trick helps Shakhtar qualify
The Brazilian bagged a hat-trick in the 5-2 Group E win in the Danish capital but the game turned on an unsavoury episode after 26 minutes.
Seemingly unaware that his team mate Willian was attempting to play the ball back to Nordsjaelland's goalkeeper after Morten Nordstrand had received treatment, Adriano pounced on the pass to slot home and make it 1-1.
"Their attacker didn't get it," Nordsjaelland captain Nicolai Stokholm told reporters.
"I looked down at my armband, and there's something about respect - it has to be said we didn't see much of that.
"We thought that they would give us a goal. Half their team seemed to think so too, but the other half didn't."
Luiz Adriano's effort, which cancelled out Nordstrand's deft volleyed opener for the Danes, led to an angry reaction from the Nordsjaelland players and was greeted with jeers and whistles from the incredulous home crowd.
Any thoughts the Danes might have had of being allowed to score unopposed were soon dashed as Taras Stepanenko dispossessed Nicolai Stokholm as he advanced on goal from the ensuing kick-off.
"I hope my boy was in bed by the time Shakhtar scored a goal of that character - that sort of thing doesn't belong anywhere," said Nordsjaelland sporting director Jan Laursen, whose modest Danish champions had been enjoying their first taste of elite European action until Tuesday's incident.
Incensed by the goal, Nordsjaelland poured forward and snatched back the lead when Kasper Lorentzen turned and rifled home in the 29th minute.
However, Ukraine's Shakhtar were the better side and went about the task of dismantling the Danish challenge.
Brazilian playmaker Willian scored a brilliant brace either side of half-time, including a stunning curled effort from the edge of the box, to put his side in the driving seat.
Luiz Adriano added two more to complete his hat-trick before being replaced in the 81st minute, with the boos of the home crowd ringing in his ears.
Shakhtar top the group on 10 points, one ahead of Juventus who beat Chelsea 3-0 in Turin.
Despite being out of the race, Nordsjaelland can still play a part in deciding who qualifies with the 2009 UEFA Cup winners as they face struggling holders Chelsea in London in their final group game on December 5.
Shakhtar host Juve looking to wrap up top spot to rubberstamp their burgeoning reputation as Champions League contenders despite the controversy in Copenhagen, which could still lead to consequences if UEFA becomes involved.