Nicely-crafted first-half goals by Dimitar Berbatov and Michael Owen underlined the visitors' dominance and Antonio Valencia's stunning strike on 48 minutes put the result beyond any doubt.
"The laughter and the jokes have quietened down a little bit. It was a big kick in the teeth as everyone knows," former Real Madrid striker Owen told Sky Sports of how his team mates have reacted to Sunday's humbling.
"We were a little bit under pressure after the result on the weekend. Although no one here started on the weekend we had United's reputation to look after. Roll on Everton now," added Owen.
Manager Sir Alex Ferguson was visibly relieved and will hope for a similar performance against Everton in the Premier League on Saturday.
"I think we tried to play the history books on Sunday. That's the nature of Manchester United, we try and win whether it's with 10 men or nine," said Ferguson.
Elsewhere in the League Cup, Arsenal withstood a late Bolton Wanderers onslaught to overcome their Premier League rivals 2-1.
Goals from Andrei Arshavin on 53 minutes and Park Chu-young (56) came in quick reply to Fabrice Muamba's 47th-minute opener.
In the two all-Championship matches, Cardiff saw off Burnley 1-0 and Crystal Palace beat division leaders Southampton 2-0.
In Wednesday's League Cup matches, Manchester City visit Wolverhampton Wanderers, third-placed Chelsea travel to Everton, Liverpool play away at Stoke City and Newcastle United go to Blackburn Rovers.
The quarter-final draw takes place on Saturday.
