Parkinson's men, along with York City, Rochdale and Chesterfield, were awarded byes this Monday morning from the North East section of the competition.
The teams also selected in the North East section and who will have to start at round one are:
Barnsley
Burton Albion
Doncaster Rovers
Hartlepool United
Mansfield Town
Notts County
Scunthorpe United
Sheffield United
Burton Albion
Doncaster Rovers
Hartlepool United
Mansfield Town
Notts County
Scunthorpe United
Sheffield United
The club's bye means City are now scheduled to enter the Johnstone's Paint Trophy at the second round stage, which this year takes place on Tuesday 6 October 2015.
The draw for round two of the JPT is scheduled for Saturday 5 September 2015.