Second round matches will be played on the weekend of December 4 with specific dates and kick-off times dependent on the live television broadcast selections.
The draw took place live on ITV4 following Salford City’s 1-0 win at Dagenham & Redbridge.
After drawing 2-2 with Wycombe Wanderers on Saturday afternoon, Pools will have to beat the League One side in a replay at Adams Park on Tuesday in order to progress.
The winners of the replay will receive £22,629 in prize money and have the opportunity to win a further £34,000 with victory in the second round.
Following Saturday’s draw, Hartlepool interim manager Antony Sweeney told The Mail: “We need to be in the hat, that’s the minimum expectation but we’re disappointed having took the lead twice and we felt like we did enough to win the game.
"Sometimes you’ve got to look and go we’ve come up against a League One side who are flying high and we’re in the Championship last season, yes they made a few changes but they’re a team who have put a lot of teams under pressure.
"The fact that we were so competitive and are disappointed not to have won is a positive.”
Second round draw in full…
Yeovil Town v MK Dons or Stevenage
Oxford United/Bristol Rovers v Sutton United
Burton Albion v Port Vale
Buxton v Morecambe
Lincoln City v Hartlepool United or Wycombe Wanderers
AFC Wimbledon v Gillingham or Cheltenham Town
Colchester United v Wigan Athletic or Solihull Moors
Leyton Orient v Tranmere Rovers
Northampton Town or Cambridge United v Bradford City or Exeter City
Doncaster Rovers v Mansfield Town
Walsall v Swindon Town
Rotherham United v Bolton Wanderers or Stockport County
Gateshead or Altrincham v Charlton Athletic
Boreham Wood v St Albans City
Kidderminster Harriers v FC Halifax Town
Carlisle United v Shrewsbury Town
Salford City v Chesterfield
Rochdale or Notts County v Sheffield Wednesday or Plymouth Argyle
Ipswich Town or Oldham Athletic v Barrow
Portsmouth v Harrogate Town