Juventus' 1-0 win at Shakhtar Donetsk condemned the London club to third place in Group E but at least Chelsea departed with some pride as Fernando Torres scored twice to give Rafael Benitez his first taste of victory since replacing Roberto Di Matteo as manager last month.
Benitez was again heckled and Di Matteo's name was sung around the stadium on a subdued night that came to life with a burst of three penalties in the first half.
Both sides missed one before David Luiz showed how to do it from the spot in the 38th minute and Torres made it 2-0 on the stroke of halft-ime, the 50 million-pound striker netting only his second goal in two months.
Joshua John scored for Nordsjaelland immediately after half-time but Gary Cahill with a header, Torres again and Juan Mata with a close-range effort put Chelsea in control before Oscar ran through to score as Nordsjaelland capitulated.
It was all academic, though, and the final 25 minutes of Chelsea's Champions League campaign resembled a friendly as news from Ukraine filtered in and Shakhtar went through on a better head-to-head record against the Londoners.
Rarely can a 6-1 victory have been celebrated in near silence as fans drifted away to contemplate Thursday nights watching their side in the Europa League for the first time.
"We had to do our job and as a manager you have to pleased with the performance of the team," interim manager Benitez, who had managed two draws and a defeat in his first three games in charge, told reporters.
"We had 32 attempts at goal, 18 on target and six goals so there are a lot of positives but we have to be disappointed because we wanted to progress in the Champions League."
"I'm not surprised Juventus won because they are a good team. It was out of our hands.
"It was important to win but also the way we won and the way we played. We saw character, attitude, commitment and intensity so I'm pleased for them, for the fans, and for me."
A win would have put Chelsea through if Shakhtar had also won at home against Juventus and when Torres made it 2-0, racing on to a Victor Moses through ball before scoring at the second attempt, the fans began to shout "Come on Shakhtar".
It was a forlorn hope, though, as Chelsea paid the price for their 2-1 defeat in Donetsk and conceding twice in a single-goal victory at home to the Ukraine champions when Di Matteo, the man who led the club to their first European Cup, was in charge.
"We can't turn the clock back," Benitez said. "Now we'll go and try to win the Europa League."
After a run of six games without a win the match kicked off in a strange atmosphere after mild booing for Benitez as he took his seat and virtual silence when the goal-shy Torres's name was read out by the announcer.
Chelsea threatened early with Moses forcing a sharp, low save from Jesper Hansen after connecting sweetly with Ashley Cole's cross. There were ironic cheers when Torres had the ball in the net but he had already been rightly flagged offside.
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