Manchester United boss Sir Alex Ferguson was pleased to see a more disciplined display by his side as they .
The 3-0 win follows Sunday's 6-1 trouncing by Manchester City - a performance Ferguson called "suicidal".
"The nature of Manchester United is to go and win the game, whether it's eight men, nine men, 10 men," he said.
"But tonight they kept their discipline, kept their professionalism - the players enjoyed that."
Having changed his entire starting XI, Ferguson was delighted as goals by Dimitar Berbatov, Michael Owen and Antonio Valencia earned the victory.
Defender Phil Jones was the only player in the squad at Aldershot's Recreation Ground to have played any part against Manchester City.
Although Dean Holdsworth's team had chances to score and had some good possession in the second half, Berbatov's 15th-minute opener settled the four-time League Cup winners before Owen scored just before half-time to help send them through to the last eight.
Ferguson was wary of the potential for another blow after Sunday's humiliation, and highlighted how hard Aldershot made his team work.
"Aldershot take a lot of credit because they kept pressing the ball and they worked their socks off and made us play," he told BBC Sport.
"It was an important night for us in that respect because in cup ties you can easily get knocked out - all it needs is a slice of luck. We're into the next round and that's the important issue."
Ferguson said he was pleased with the players who came into the team, including Tom Cleverley, who returned after an injury picked up in September, and Nemanja Vidic, who was rested against City on Sunday.
"I have a fantastic squad and it's been difficult for some because the team's consistency this season has been very good," he added.
"But we have a long season ahead and players like Valencia and Vidic got a good 90 minutes and I'm pleased about that because [Vidic] really needed that.
"Even early on I thought he was blowing hard - I think he always needed a game and that will bring him on a ton.
"Berbatov had a great game tonight, too, and Park Ji-sung, as he always does, had a tremendous work-rate and passing ability. The big bonus was to bring back Tom Cleverley."
Aldershot boss Holdsworth said he was content with his team's performance, despite the scoreline.
"I'm proud of their effort," he said. "They worked extremely hard and there's a lot to learn from playing against sides like that.
"When my players look at what the best do, there are a few lessons there. With my respect for Manchester United and the effort the boys put in, it was a fantastic occasion for the club."
The former Brentford, Wimbledon and Bolton player added: "We want more of this."