The game between Manchester United and Bournemouth was called off after the item was discovered close to kick-off.
A controlled explosion was carried out on the device, which police said was accidentally left by a private firm.
Greater Manchester Mayor and Police and Crime Commissioner Tony Lloyd called for a full inquiry into the "fiasco".
Bomb disposal experts were called to the 75,000-seat stadium on Sunday after the replica device was found in a toilet.
The Premier League match has been rearranged for Tuesday at 20:00 BST and will be screened live by Sky Sports.
Lloyd called the situation "unacceptable" and demanded an inquiry to discover "how this happened, why it happened and who will be held accountable".
He added that "this fiasco" had:
◾"Caused massive inconvenience to supporters who had come from far and wide to watch the match";
◾"Wasted the time of huge numbers of police officers and the army's bomb squad";
◾"And unnecessarily put people in danger."
The Premier League praised the way the incident was dealt with.
A statement read: "We would like to thank Manchester United's staff, the police and other emergency services for all their efforts today as well as rearranging the match for this coming Tuesday.
"Both Manchester United and AFC Bournemouth's management has been extremely helpful in reaching a swift resolution, which is the best possible given today's events."
United will refund all tickets and allow ticket holders from both clubs to watch Tuesday's re-arranged game for free, while Manchester United season ticket holders will also be given a credit.
It is a gesture that is estimated will cost United around £3m.
Bournemouth expect to make an announcement on Monday about travel arrangements for their fans.