Despite a valiant effort in a thrilling second leg at Swindon's County Ground, United drew 5-5 against Mark Cooper's Robins, meaning they lost 7-6 on aggregate.
The final two places in League 1 for the 2015/2016 campaign will now be taken up by the loser in the League 1 Play-Off Final between Swindon and Preston North End and the winner of the League 2 Play-Off Final.
The full list of twenty teams confirmed in League 1 next season along with City looks like this:
Barnsley
Blackpool
Burton Albion
Bury
Chesterfield
Colchester United
Coventry City
Crewe Alexandra
Doncaster Rovers
Fleetwood Town
Gillingham
Millwall
Oldham Athletic
Peterborough United
Peterborough United
Port Vale
Rochdale
Scunthorpe United
Sheffield United
Shrewsbury Town
Walsall
Wigan Athletic