Steaua, who beat Barcelona 2-0 on penalties in the final of the 1986 European Cup, won the second leg 1-0 at Rosenborg Trondheim but the Norwegians went through 3-1 on aggregate.
The Romanians are fifth in their domestic league, four points behind leaders Astra after eight matches.
A 28th-minute goal by Morten Rasmussen led Danes Midtjylland to a 1-0 victory as Ronald Koeman's out-of-sorts Southampton were eliminated 2-1 on aggregate.
Southampton are third from bottom in the Premier League, having failed to win any of their opening three games of the season.
Elsewhere, a hat-trick by Marco Reus and two goals from Shinji Kagawa helped Borussia Dortmund thump Norwegian club Odd 7-2 as the Bundesliga side scored a runaway 11-5 aggregate triumph.
The draw for the group stages will be held in Monaco on Friday.
(Writing by Tony Jimenez,; Editing by Pritha Sarkar)
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