United avoided further humiliation following Sunday's 6-1 thrashing at Old Trafford thanks to a 3-0 victory at Aldershot.
They were never in any real danger of suffering one of the greatest cup upsets of all time, with goals from Dimitar Berbatov, Michael Owen and Antonio Valencia wrapping up victory shortly after half-time at the EBB Stadium.
Manager Ferguson told Sky Sports afterwards: "Obviously, we had a difficult day on Sunday simply because we tried to play the history book.
"The nature of Manchester United is to go and win the game, whether it's eight men, nine men, 10 men or seven men.
"That's their nature and it's very difficult to change that.
"But tonight they kept their discipline, they kept their professionalism, enjoyed it tonight - the players enjoyed that."
Ferguson changed his entire starting XI tonight, with Phil Jones the only player in the matchday squad who featured in Sunday's game.
Tom Cleverley made his comeback from injury and captain Nemanja Vidic also returned, while several of Ferguson's fringe men put their hands up for a starting spot in Saturday's Barclays Premier League game at Everton.
He added: "They'll always give me nudges. It's difficult picking a team when you've got so many good players.
"We have a fantastic squad. That's why I had to play these players tonight. They need the games, they've not had many first-team games to be honest with you because the consistency of the team has been very good - we've not needed to make any changes.
"But there's Michael Owen - every time he plays, he scores. It's a fantastic record he's got.
"He's a fantastic professional. Dimitar Berbatov had a fantastic game tonight and scored a tremendous goal from great football.
"So they've all done well, Valencia, Thomas Cleverley back is a good thing for us because the boy's an outstanding footballer.
"Vida's got another 90 behind him. I think he needed it. Until he got his breathing going, he was feeling it."
Owen, who scored his third goal in two League Cup ties this season, said: "We were a little bit under pressure with the result at the weekend.
"Although no-one here started at the weekend, you still have Manchester United's reputation to look after.
"So whatever side was put out, we wanted to bounce back and thankfully we got the win.
"As you can imagine, the laughs and jokes have quietened down a little bit (since Sunday).
"Sometimes you need a kick in the teeth to get going and it was a big kick in the teeth, as everybody knows, and we were eager to bounce back."
Ferguson was full of praise for Tuesday night's opponents.
"Aldershot fought really hard," he said.
"They take a lot of credit, they never stopped running or pressing the ball. They put a good shift in.
"We showed our quality at times, could've maybe scored a few towards the end of the match when they were tired.
"We satisfied. With cup ties, the main important thing is to win the game. We're into the next round now."
Aldershot boss Dean Holdsworth, who shared the traditional glass of wine with Ferguson after the match, was delighted with his side's attempt to bridge the gulf between npower League Two also-rans and the Premier League champions.
"I'm very proud," he said. "We can learn a lot from the game. The fans were magnificent and the team will be hungry for more occasions like this.
"It's been fantastic. What a team Sir Alex put out in front of us.
"United had bundles of quality but we'll learn from that.
"We were beaten by a set of world-class players and it was a joy to face them.
"We'll be pleased tomorrow when we wake up.
"Sir Alex was full of compliments saying, 'You should be proud of your boys', and we'll take comfort from that."