The odds had been stacked against Jim Gannon's men who headed into the clash trailing 3-0 from the first leg, but youngster Ross Forbes provided hope with a 17th-minute strike before the SPL side were controversially denied a penalty.
Rather than Motherwell closing the gap, it was Steaua's Petre Marin who converted from the spot after the break before a double from Bogdan Stancu killed off any hope of a dramatic comeback.
Motherwell made three changes from the side who lost in Romania, with Steven Hammell, Jamie Murphy and Jim O'Brien drafted into the side in place of Steven Saunders, Steve Jennings and Chris Humphrey, who were all named on the bench.
An own goal from Stephen Craigan and goals from Banel Nicolita and Stancu gave the visitors an impressive advantage from the first leg of the third qualifying round, with Steaua simply too strong for Motherwell on their own territory.
The Romanians tried to exert their authority on this match early on by forcing a corner in the opening minutes. Nicolita delivered the ball into the box and it broke kindly for Rafal Grzelak but his effort was blocked by Craigan.
Gannon had emphasised the importance of an early goal to Motherwell if they were to have any hope of salvaging the tie, and the home side gradually imposed themselves upon the game and began to look like the superior side.
Forbes, who netted twice against Albanians Flamurtari in the last round, tried his luck with an audacious long-range shot from the left flank which forced a decent one-handed save from Rufay Zapata.
The goalkeeper was then called into action to block a powerful header from John Sutton, before swiping a swerving shot from Murphy to safety.
However, he was left plucking the ball out of the back of the net with 17 minutes gone. Paul Slane's corner kick found Forbes out on the left and he caught Zapata off guard with a superb shot from 25 yards which clipped the post en route to the top corner.
The 19-year-old then attempted to turn goal provider when he presided over a free-kick a few yards outside the area before picking out Sutton, but the striker nodded wide from six yards.
Motherwell could have claimed another goal 10 minutes before the break - and bolstered further their hopes of a comeback - when a shot from Murphy appeared to be handled by Sorin Ghionea but their pleas were dismissed by Spanish referee Carlos Gomez.
Instead, the Steelmen were forced to head into the interval with a single-goal advantage on the night, with the match officials leaving the pitch to jeers from the crowd still furious at the controversial call.
Motherwell started the second half strongly with Forbes threatening again from another set-piece, this time drawing a superb punched clearance from Zapata, before Mark Reynolds screwed the rebound wide of the target.
Hopes of clawing back the deficit were dealt a crushing blow when Steaua restored parity from the penalty spot after 54 minutes.
O'Brien was judged to have fouled Stancu and this time the referee did not hesitate to point to the spot before Marin converted for the Romanians.
The Fir Park side battled on and Zapata was called into action again, this time blocking from substitute Robert McHugh.
But the tie was well and truly over as a contest after 67 minutes when Stancu collected the ball 35 yards out in plenty of space and lashed high into the net with a superb strike, which left John Ruddy with no chance in the Motherwell goal.
Stancu then heaped further misery on the hosts when he drove home an angled shot with six minutes remaining to put the gloss on the victory for the Romanians.