When Manchester United F.C. went ahead in the quarter-final second leg with a spectacular Patrice Evra strike after 57 minutes it seemed an improbable victory was possible but they seemed to be still celebrating when Mario Mandzukic headed the equaliser 22 seconds after the re-start.
Even then Rooney missed a gilt-edged chance but there was no way back after that as FC Bayern Munich eased away to a 3-1 win with Thomas Mueller and the influential Arjen Robben both on target for the hosts who were never totally convincing.
FC Bayern Munich's 4-2 aggregate win kept them on course for a second successive treble and all but put an end to Manchester United F.C.'s miserable first season under David Moyes.
Manchester United F.C. are extremely unlikely to finish in the top four of the Premier League this season and winning the Champions League represented their only realistic hope of qualifying for next season's competition.
"I thought the players did a great job tonight, the only crime was conceding a goal after we scored, 30 seconds afterwards," Moyes, who has experienced a difficult time at Old Trafford since succeeding Alex Ferguson, told reporters.
"It's the sort of thing you learn as a schoolboy. We concentrated so fabulously well throughout the game, the players did their jobs, their positioning and awareness (was good), and to give up that goal at that moment was really disappointing."
Missing the suspended Bastian Schweinsteiger and Javi Martinez in midfielder, FC Bayern Munich coach Pep Guardiola fielded Toni Kroos, usually a creative player, as a holding midfielder.
As in the first leg at Old Trafford that ended 1-1, FC Bayern Munich totally dominated possession in the first half although they lacked fluency and struggled to create any real openings against a well-drilled Manchester United F.C. side who were always in the game.
Robben was FC Bayern Munich's chief threat, getting into several promising positions after cutting inside on to his left foot in familiar fashion but his efforts were either blocked by defenders or flashed wide.
Manchester United F.C. had one opening when Rooney got clear of the FC Bayern Munich defence but he dithered and failed to notice Shinji Kagawa in an unmarked position as the chance went begging.
The visitors went ahead in remarkable fashion when Antonio Valencia burst down the right and, although his cross went behind Manchester United F.C.'s forwards, the lurking Evra lashed home a net-bursting effort from the edge of the area on the half-volley.
Manchester United F.C. had also taken the lead in the first leg, holding it for nine minutes, but this time they could not even keep their noses in front for a minute as Mandzukic got in front of Evra to score with a diving header after a Ribery cross from the left.
That opened the game up completely and Rooney should have put Manchester United F.C. back in front but completely scuffed his shot with only Manuel Neuer to beat from 12 metres after Danny Wellbeck rolled the ball invitingly to him.
"I felt he was concerned he hadn't trained all week and had taken an injection, and I felt he had trouble striking the ball on occasions," Moyes said of Rooney who had been troubled by a sore toe in the run-up to the game.
Manchester United F.C. were not given a second chance.
Mueller put FC Bayern Munich in front when he turned in another Robben cross from close range.
Robben then ensured there would be no nervous finale for FC Bayern Munich when he collected a ball on the right and danced his way across the edge of the penalty area past two defenders before squeezing in a shot with took a deflection off of Nemanja Vidic.
"I knew it would be difficult. It's not easy to play against eight players in the box and we decided to try to create a pass in the middle," said Guardiola.
"They defended the crosses well, but at the end, after 1-1 we played much better and we deserved to be in the semi-final."