In the first of two semi-finals in the space of four days – Boro play West Ham in the last four of the FA Cup on Sunday – Steve McClaren's side never really found their feet and fell to a 30th minute goal by the impressive Nicolae Dica.
Without injured duo Gareth Southgate and Chris Riggott at the back, Boro's makeshift defence was caught napping on the half-hour mark.
Fabio Rochemback failed to close down Mirel Radoi on the edge of the box and the Steaua skipper was given the space to flick a harmless looking long throw into the danger area.
Dica showed great awareness to pull away George Boateng before drilling a 12-yard shot on the turn into the top corner of the net past the despairing dive of Mark Schwarzer.
Boro finally settled towards the end of the first period and Yakubu looped a downward header on to the top of the bar before James Morrison was denied at the back post by keeper Carlos Alberto Fernandes.
With their goal safely in the bag the home side sat back after the break and allowed Boro plenty of possession.
But with Yakubu and Jimmy Floyd Hasselbaink struggling to break down a solid looking Steaua defence and the arrival of Massimo Maccarone and Ray Parlour off the bench having little effect, Boro never really looked like scoring a priceless away goal.
Indeed it could have been worse for the away side had Schwarzer not pulled off two excellent saves from Nicolae Goian and Dica halfway through the second period.
Boro also had a lucky escape when Schwarzer and Ugo Ehiogu collided competing for the same cross and Goian failed to force the ball home from close range.
Maccarone, who scored the dramatic late winner against FC Basel in the last round, almost pulled Boro level with a deflected shot right at the death but had that gone in it would have been rough justice on a Steaua side who looked in command throughout.