United booked their place in the second round with a dramatic 4-3 extra-time win over local rivals Lincoln on Tuesday night.
Saturday's draw was made by former players Matt Le Tissier and Phil Thompson.
The eight Premier League teams who are competing in Europe enter the competition at the third round stage.
Draw in full:
Leeds v Barnet
Watford v Accrington Stanley
Crewe v Wigan Athletic
Doncaster v Derby County
Sheffield United v Bury
Millwall v Southampton
West Brom v Cheltenham
Peterborough v Everton
Hereford v Leicester
Port Vale v QPR
Fulham v Wycombe
Hull City v Hartlepool
Walsall v Bolton
Middlesbrough v Notts County
Charlton v Carlisle
Barnsley v MK Dons
Chesterfield v Manchester City
Scunthorpe v Aston Villa
Southend v Brighton
Brentford v Luton
Reading v Darlington
Birmingham v Wrexham
Rotherham v Norwich
Mansfield v Portsmouth
Leeds v Barnet
Watford v Accrington Stanley
Crewe v Wigan Athletic
Doncaster v Derby County
Sheffield United v Bury
Millwall v Southampton
West Brom v Cheltenham
Peterborough v Everton
Hereford v Leicester
Port Vale v QPR
Fulham v Wycombe
Hull City v Hartlepool
Walsall v Bolton
Middlesbrough v Notts County
Charlton v Carlisle
Barnsley v MK Dons
Chesterfield v Manchester City
Scunthorpe v Aston Villa
Southend v Brighton
Brentford v Luton
Reading v Darlington
Birmingham v Wrexham
Rotherham v Norwich
Mansfield v Portsmouth
