Chelsea were held by Olympiakos after an unconvincing display in the first leg of their Champions League last-16 tie on a cold night in southern Greece.
Drogba (centre) failed to make an impression on his return from Africa
John Terry and Frank Lampard were left on the bench but the Blues were largely untroubled in a quiet first half in which Ricardo Carvalho went closest.
The visitors showed more ambition after the break but failed to create much.
Salomon Kalou shot tamely at the keeper when through late on and Chelsea will hope for much better in a fortnight.
With their formidable home record, they will be favourites to reach the semi-finals for the fourth time in five seasons.
But even though the competition's meanest defence recorded a fifth straight clean sheet, the fare served up in unseasonably harsh weather for Greece hardly set the pulses racing.
Olympiakos have plenty of experience and nous about them, with an average age of a shade over 30 in their starting line-up and 10 league titles in 11 years.
Chelsea were happy to concede possession to them and while Predrag Djordjevic and Luciano Galleti buzzed around early on to keep England left-back Ashley Cole busy, the final ball was often lacking.
At the other end, the Blues appeared to have the edge in terms of pace and movement off the ball.
Florent Malouda's snapshot was well saved by 36-year-old keeper Antonis Nikopolidis, who also kept out Carvalho's firm header after Juliano Belletti's deep free-kick was flicked on by Malouda.
The visitors had a scare moments later when Djordjevic's corner was helped on by Ieroklis Stoltidis' head but Vassilis Torosidis failed to make clean contact.
Having seen what Olympiakos had to throw at them in the first period, the Blues showed greater desire to commit men forward after the break, with Ashley and Joe Cole featuring more prominently than they had earlier.
But with Didier Drogba appearing to struggle with a tight hamstring on his comeback after African Nations duty, they lacked a cutting edge.
Indeed, Chelsea needed keeper Petr Cech to save low down in his first meaningful action in the 57th minute when Galletti teed the ball to Djordjevic from a free-kick.
Kalou, Nicolas Anelka and, belatedly, Lampard were introduced by Avram Grant in a bid to find some sharpness in the final third but they failed to make much of an impression on the home defence.
Kalou could still have won it right at the end but his control let him down badly and he shot weakly at Nikopolidis to sum up his team's efforts.
Olympiakos: Nikopolidis, Zewlakow, Julio Cesar, Antzas, Pantos, Ledesma, Galletti (Leonardo 83), Torosidis, Djordjevic (Belluschi 76), Stoltidis, Kovacevic (Leonel Nunez 87).
Subs Not Used: Sifakis, Patsatzoglou, Mitroglou, Sisic.
Chelsea: Cech, Belletti, Carvalho, Alex, Ashley Cole, Essien, Makelele, Ballack (Lampard 86), Malouda (Kalou 75), Drogba, Joe Cole (Anelka 75).
Subs Not Used: Cudicini, Obi, Wright-Phillips, Terry.
Booked: Alex, Belletti, Makelele, Ashley Cole.
Ref: Konrad Plautz (Austria).
BBC Sport Player Rater man of the match: Chelsea's Petr Cech 6.81 (on 90 minutes).
• Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.