The Red Devils - finalists in each of the last two years - raced into a 3-0 lead at Old Trafford courtesy of Darron Gibson's early opener and a brace from Nani, and appeared to be coasting into the semi-finals.
However, Ivica Olic's goal just before the break set up a nervy second period, and after Rafael picked up his second booking the German outfit took control and deservedly grabbed the decisive away goal with Arjen Robben volleying home in stunning style.
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"The key point in the game was red card. No doubt about it," Ferguson told ITV.
"They would never have got through if we'd had 11 on the field. Young boy, bit of inexperience. They got him sent off. Everyone sprinted towards the referee - typical Germans. You cannot dispute that, they are like that."
But he added: "Our problem was they had the extra man, they made the ball work. I thought we defended very well. It took an excpetional goal to end the tie really. It was a tremendous hit by Robben."
He also praised his team's performance despite their exit which ended their hopes of a third successive final.
"I think we have performed very well. Our performance today was excellent. It was a great performance. We were very, very unlucky."
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