Chelsea were not at the races from the word go, and found themselves behind just after the half-hour mark after a hotly disputed penalty was given to the home side.
Ryan Bertrand was adjudged to have fouled danger man Raul Rusescu as he went up for a header, and the top scorer in the Romanian league got up to take the spot-kick himself, smashing the ball under Petr Cech.
Although they initially looked to have woken up after falling behind, Chelsea toiled away, but could not find that cutting edge all evening, and will have to do much better in the return leg at Stamford Bridge.
The reigning European champions looked anything but on the night, starting the game sluggishly, with Fernando Torres receiving little service up front.
Just after the half hour, Bertrand's efforts to beat Rusescu to the ball after getting the wrong side of the hitman resulted in the Romanians getting the chance to take a deserved lead from the spot.
Cech will be disappointed after guessing the right way, but the power Rusescu put on the penalty was enough to beat the unfortunate keeper.
The goal seemed to spark Chelsea into life, creating their best chance of the game almost straight away.
Yossi Benayoun played a neat one-two with Oscar, engineering space on the edge of the box, but Ciprian Tatarusanu in the Bucharest goal got down well to his right to tip the Israeli's tame effort wide.
The second period was a very cagey affair, with attacks breaking down too easily for Rafael Benitez's liking.
Juan Mata was brought on to try and inject some quality into the tie, but even he was having an off night.
Another substitute, Marko Marin, had Chelsea's best attempt at an equaliser, cutting inside well from the left, and forcing a smart save from Tatarusanu.
The very quiet Eden Hazard fired over from a tight angle, and David Luiz's powerful free-kick from distance worried Tatarusanu, but on the night the Blues were just not good enough.