United will be expected to begin the defence of their trophy with victory over a Burton side who have lost three of their first four games in the Championship.
But Liverpool face a stiff task in travelling to Leicester, one of four all-Premier League ties.
The others see Manchester City visit West Brom, a south coast derby between Bournemouth and Brighton, and Crystal Palace home to Premier League new boys Huddersfield Town.
Town stunned Palace 3-0 at Selhurst Park on the opening day of the season.
United and the other teams in European competition only enter the draw for the League Cup, dubbed the Carabao Cup this season after its new sponsors, at the third-round stage.
The decision to stage the draw in Beijing infuriated fans and media in England.
Organisers said it was to help win new supporters and expand the popularity of the domestic cup in Asia.
But the draw was scheduled for 11:15 am Chinese time — 4:15 am in Britain — meaning an before-dawn wake -up call for supporters eager to know who their team were playing in ties beginning the week of September 18.
In the event, the draw began 20 minutes late, dragged on for 40 minutes and was not on television, further riling fans attempting to follow it on Twitter.
Previous draws of the League, or Carabao, Cup were dogged by mishaps.
The English Football League apologised after the first-round draw in Bangkok, which saw Charlton supposedly drawn to play Exeter away and Cheltenham at home.
The Daily Telegraph newspaper said that staging the third-round draw in the Chinese capital was «indicative of the total disrespect shown to football fans».
The League Cup was rebranded the Carabao Cup after a Thai energy drinks maker secured a three-year sponsorship deal with the English Football League in April.
Editorial