Mexican striker Javier Hernandez opened the scoring just before half-time and Park Ji-sung added a second just moments after Didier Drogba had given Chelsea hope with an equaliser on the night but United ran out 3-1 winners on aggregate.
Ferguson's side, who beat Chelsea on penalties in the 2008 final and had carved out a 1-0 lead from last week's first leg, absorbed plenty of pressure during an open and balanced game in which the Londoners had Ramires sent off with 20 minutes left.
The victory put United into their fourth semi in five years and left big question marks hanging over Chelsea manager Carlo Ancelotti's future now that his flagging team's only realistic chance of silverware has evaporated.
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United, chasing a treble of Champions League, Premier League and FA Cup, will face Schalke 04 or Inter Milan in the last four with the German side holding a 5-2 advantage over the Italians before Wednesday's quarter-final second leg.
Ferguson singled out "incredible" old-timer Ryan Giggs for an outstanding game in the centre of midfield from where he set up Hernandez's 43rd-minute opener while adding that the Mexican had almost not started as he had toyed with a different lineup.
"We had two teams picked tonight and hopefully I picked the right one, I'm not sure I did pick the right one," Ferguson told a news conference.
"The other option is to play Park in that position and Wayne (Rooney) up top, leaving Chicha (Hernandez) out. That's where you get luck, Chicharito scores the first goal."
While the loud taunts from United fans to Chelsea manager Carlo Ancelotti of "You're getting sacked in the morning" were possibly wide of the mark, the Italian is under pressure now his side's last realistic chance of silverware has vanished.
"I'm not concerned," he told a news conference when asked if he was worried about his job given owner Roman Abramovich, who was watching from the stands, has been quick to show the exit to previous managers who finish a season without a trophy.
"I have to work, I have to try to do my best. It is not my decision to stay or not stay," said Ancelotti.
Although Chelsea started brightly their cause was not helped by striker Fernando Torres' apparent lack of confidence in front of goal, which seems to be growing with every match that goes by witho
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