With the likes of Barcelona, Real Madrid and even Shakhtar Donetsk sending out real messages of intent in their last-16 ties, the game was the ideal time for Carlo Ancelotti's men to do the same against the lowest-ranked team left in the competition.
Instead, they contrived to fluff at least a dozen straightforward finishes at Stamford Bridge, allowing Copenhagen to salvage some pride after their comprehensive first-leg defeat.
Chelsea simply cannot afford to squander the kind of chances they missed if they are to make it through to the semi-finals, regardless of who they draw on Friday.
How Fernando Torres would have loved to have started up front in what appeared an ideal game in which to end his goal drought; Carlo Ancelotti deciding it was better for the Spaniard to play a substitute role ahead of Sunday's Premier League clash with Manchester City.
The tone for Chelsea's wasteful evening was set as early as the third minute when Frank Lampard sent Ashley Cole's cross wide from no more than four yards.
Cole himself then shot straight into the side-netting when he should have cut the ball back, Yury Zhirkov flashed wide after a lovely Didier Drogba backheel teed up a Cole cross, and Nicolas Anelka's poked finish was thwarted by Johan Wiland after Ramires' brilliant cross-field ball set up a quick break.
Although they could have been 4-0 down inside the opening quarter, Copenhagen were infinitely more sprightly than they had been in the first leg, before which they had not played a competitive match for three months.
Kitted out in what could only be described as hot pink jerseys, they almost made Chelsea pay for their wastefulness in the 26th minute.
John Terry, who could be forgiven for being distracted by the England captaincy farce, brought down Dame N'Doye 20 yards out and, despite being so close to goal, the Senegal striker managed to crash a brilliant free-kick against the post.
Zhirkov fluffed another close-range finish from Anelka's cutback, Drogba shanked a cross with team-mates queueing up to score and also sent more than one curling shot too close to Wiland before half-time.
Chelsea's finishing failed to improve after the restart with Drogba volleying Jose Bosingwa's whipped ball wide from six yards, John Obi Mikel nodding against the crossbar from no more than two yards and Anelka twice hesitating when clean through and allowing Copenhagen's defence to recover.
Drogba was booked for taking out his frustration on Martin Vingaard, which was Torres' cue to begin warming up on the touchline.
Ramires then made a mess of an improvised finish from Drogba's cutback before Torres was beaten to the field by Copenhagen striker Kenneth Zohore, who replaced Pierre Bengtsson.
The change had the desired effect for the visitors, with N'Doye shooting wide under good pressure from Bosingwa.
Claudemir was booked for hauling back Ramires before Torres finally made his entrance midway through the half in place of a nonplussed Anelka who was withdrawn.
A wicked deflection almost helped Torres make an instant impact and he also sent a low finish straight at Wiland after Copenhagen lost Vingaard to injury.
The midfielder was replaced by Cesar Santin, with Chelsea withdrawing Zhirkov for Florent Malouda.
N'Doye blazed another good chance over on the break as Copenhagen went for broke but they overstepped the mark when Christian Bolanos was booked for diving.
Michael Essien was thrown on for Mikel with six minutes remaining.
Torres was being urged to "shoot" by the crowd every time he got within range.
The striker's team-mates did their best to tee him up but to no avail.