Two goals from the ever-improving Javier Hernandez were enough to overcome Marseille at Old Trafford and secure their passage thanks to a 2-1 win on the night and on aggregate.
However, they had to endure a nervous end to this last-16 second leg after a Wes Brown own goal with eight minutes remaining.
Hernandez's remarkable impact has been a huge bonus for United, according to Ferguson.
He opened the scoring in the fifth minute by getting on the end of a cross from Wayne Rooney. His second in the 76th minute was almost identical with substitute Antonio Valencia supplying the delivery.
"I think we are surprised. When we bought him we thought it would take him some time to adjust first of all," Ferguson said.
"He has adjusted to the physical part very well and he is lasting 90 minutes very well now.
"Hernandez's pace and movement is helping us. He is a real handful. You see the first goal - the boy's movement is fantastic."
Ferguson's satisfaction at reaching the last eight for a fifth successive season was tempered by the fear that both John O'Shea and his replacement Rafael face a spell on the sidelines after suffering suspected hamstring injuries.
The treatment room is already filling up with Nemanja Vidic unavailable last night with a calf problem.
Rio Ferdinand, Darren Fletcher, Michael Owen, Park Ji-sung, Jonny Evans and the goalkeeper Anders Lindegaard were among those also unavailable for selection.
Ferguson could be short of numbers going into a crucial phase of the campaign with United still on course for the treble.
He was pleased with the response of the team after O'Shea and Rafael made early exits.
"The balance of the team was affected with two defenders coming off. There was a lack of experience in the team and that could have cost us. But we hung on," Ferguson said.
"They are a very powerful team and their delivery into the box was very good. They kept us under pressure a lot of times.
"When we played our football particularly in their half of the field we did OK. We always looked comfortable on the ball.
"But we just couldn't get enough of it in the second half in their half of the field. They kept us on the edge of our box a lot."
Marseille coach Didier Deschamps said: "My first feeling is one of regret. We let our chance slip and we are out.
"Manchester United are not a fantastic side and they suffered two injuries during the game. They were not at their best but we could not capitalise on that.
"But we are a young side, who are learning, and it will take time. At this level small details win you games."